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1398 lines
50 KiB
C++
1398 lines
50 KiB
C++
// Hyperbolic Rogue -- embeddings
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// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
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/** \file embeddings.cpp
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* \brief Embedding 2D geometries into 3D
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*
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* This file handles primarily embedding 2D geometries into 3D.
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*
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* The following coordinate systems are used for embedding of 2D geometries into 3D:
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*
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* - *base* coordinates are simply the coordinate in the underlying 2D geometry. They support only two dimensions.
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* - *logical* coordinates: X and Y are in the Beltrami-Klein or gnomonic model, or in horocyclic coordinates for binary-like tilings. Z coordinate is the altitude above the plane.
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* - *logical_scaled* coordinates: X and Y are scaled (and possibly rotated in the XY plane) in order to match the scale and orientation of the ambient 3D geometry. They are a linear transformation of logical.
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* - *intermediate* coordinates: they use the same assignment of coordinates as actual, but they are a linear transformation of logical scaled.
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* - *actual* coordinates: final coordinates in the ambient 3D geometry.
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*
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*/
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#include "hyper.h"
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namespace hr {
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EX namespace geom3 {
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#if HDR
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enum eSpatialEmbedding {
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seNone,
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seDefault,
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seLowerCurvature,
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seMuchLowerCurvature,
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seProduct,
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seNil,
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seSol,
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seNIH,
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seSolN,
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seCliffordTorus,
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seProductH,
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seProductS,
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seSL2,
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seCylinderE,
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seCylinderH,
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seCylinderHE,
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seCylinderNil,
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seCylinderHoro,
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seCylinderSL2
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};
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#endif
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EX vector<pair<string, string>> spatial_embedding_options = {
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{"2D engine", "Use HyperRogue's 2D engine to simulate same curvature. Works well in top-down and third-person perspective. The Hypersian Rug mode can be used to project this to a surface."},
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{"same curvature", "Embed as an equidistant surface in the 3D version of the same geometry."},
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{"lower curvature", "Embed as a surface in a space of lower curvature."},
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{"much lower curvature", "Embed sphere as a sphere in hyperbolic space."},
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{"product", "Add one extra dimension in the Euclidean way."},
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{"Nil", "Embed Euclidean plane into Nil."},
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{"Sol", "Embed Euclidean or hyperbolic plane into Sol."},
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{"stretched hyperbolic", "Embed Euclidean or hyperbolic plane into stretched hyperbolic geometry."},
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{"stretched Sol", "Embed Euclidean or hyperbolic plane into stretched Sol geometry."},
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{"Clifford Torus", "Embed Euclidean rectangular torus into S3."},
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{"hyperbolic product", "Embed Euclidean or hyperbolic plane in the H2xR product space."},
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{"spherical product", "Embed Euclidean cylinder or spherical plane in the H2xR product space."},
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{"SL(2,R)", "Embed Euclidean plane in twisted product geometry."},
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{"cylinder", "Embed Euclidean cylinder in Euclidean space."},
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{"hyperbolic cylinder", "Embed Euclidean cylinder in hyperbolic space."},
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{"product cylinder", "Embed Euclidean cylinder in H2xR space."},
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{"Nil cylinder", "Embed Euclidean cylinder in Nil."},
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{"horocylinder", "Embed Euclidean as a horocylinder in H2xR space."},
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{"SL2 cylinder", "Embed Euclidean as a cylinder in twisted product geometry."},
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};
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EX bool clifford_torus_valid() {
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#if CAP_RUG
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rug::clifford_torus ct;
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ld h = ct.xh | ct.yh;
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return !(sqhypot_d(2, ct.xh) < 1e-3 || sqhypot_d(2, ct.yh) < 1e-3 || abs(h) > 1e-3);
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#else
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return false;
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#endif
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}
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EX string why_wrong(eSpatialEmbedding sp) {
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string ans = "";
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if(among(sp, seNil, seCliffordTorus, seProductH, seProductS, seSL2) || any_cylinder(sp)) {
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if(!PURE)
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ans += " pure";
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if(!meuclid)
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ans += " E";
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if((sp == seProductS || any_cylinder(sp)) && !quotient)
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ans += " cyl";
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if(sp == seCliffordTorus && !clifford_torus_valid())
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ans += " torus";
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}
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if(among(sp, seSol, seNIH, seSolN)) {
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if((meuclid && !PURE) || !bt::in()) ans += " pure or bin";
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}
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return ans;
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}
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EX eSpatialEmbedding spatial_embedding = seDefault;
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EX ld euclid_embed_scale = 1;
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EX ld euclid_embed_scale_y = 1;
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EX ld euclid_embed_rotate = 0;
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EX bool auto_configure = true;
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EX bool flat_embedding = false;
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EX bool inverted_embedding = false;
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EX bool apply_break_cylinder = true;
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EX ld euclid_embed_scale_mean() { return euclid_embed_scale * sqrt(euclid_embed_scale_y); }
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EX void set_euclid_embed_scale(ld x) { euclid_embed_scale = x; euclid_embed_scale_y = 1; euclid_embed_rotate = 0; }
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EX bool supports_flat() { return among(spatial_embedding, seDefault, seProductH, seProductS); }
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EX bool supports_invert() { return among(spatial_embedding, seDefault, seLowerCurvature, seMuchLowerCurvature, seNil, seSol, seNIH, seSolN, seProductH, seProductS) || any_cylinder(spatial_embedding); }
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EX vector<geometryinfo> ginf_backup;
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EX eGeometryClass mgclass() {
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return (embedded_plane ? ginf_backup : ginf)[geometry].g.kind;
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}
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EX eGeometryClass ggclass() {
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return (flipped ? ginf_backup : ginf)[geometry].g.kind;
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}
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EX bool any_cylinder(eSpatialEmbedding e) {
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return among(e, seCylinderE, seCylinderH, seCylinderHE, seCylinderHoro, seCylinderNil, seCylinderSL2);
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}
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EX bool in_product() {
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return ggclass() == gcProduct;
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}
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EX bool flipped;
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EX geometry_information* unflipped;
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EX void light_flip_geom() {
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indenter ind(2);
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swap(ginf[geometry].g, geom3::ginf_backup[geometry].g);
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swap(ginf[geometry].flags, geom3::ginf_backup[geometry].flags);
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if(fake::in()) {
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// println(hlog, "warning: flipping while still in fake");
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FPIU(light_flip_geom());
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}
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// hyperbolic arcm needs gNormal for cdata. Also swap gSphere and gEuclid for compute_geometry
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else if(arcm::in()) {
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dynamicval<eGeometry> g(geometry, gNormal); light_flip_geom();
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geometry = gSphere; light_flip_geom();
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geometry = gEuclid; light_flip_geom();
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}
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}
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EX void light_flip(bool f) {
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if(f != flipped) {
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if(!flipped) cgip->use_count++;
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if(!flipped) unflipped = cgip;
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light_flip_geom();
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flipped = f;
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if(!flipped) cgip = unflipped;
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if(!flipped) cgip->use_count--;
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}
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}
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#if HDR
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template<class T> auto in_flipped(const T& f) -> decltype(f()) {
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light_flip(true);
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finalizer ff([] { light_flip(false); });
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return f();
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}
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template<class T> auto in_not_flipped(const T& f) -> decltype(f()) {
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light_flip(false);
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finalizer ff([] { light_flip(true); });
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return f();
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}
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#define IPF(x) geom3::in_flipped([&] { return (x); })
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#endif
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EX void apply_always3() {
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if(!vid.always3 && !ginf_backup.empty()) {
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ginf = ginf_backup;
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ginf_backup.clear();
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}
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if(vid.always3 && ginf_backup.empty()) {
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ginf_backup = ginf;
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for(geometryinfo& gi: ginf)
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apply_always3_to(gi);
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}
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}
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EX void apply_always3_to(geometryinfo& gi) {
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auto &g = gi.g;
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if(vid.always3 && g.gameplay_dimension == 2 && g.graphical_dimension == 2) {
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/* same-in-same by default */
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auto og = g;
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g.graphical_dimension++;
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g.homogeneous_dimension++;
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g.sig[3] = g.sig[2];
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g.sig[2] = g.sig[1];
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bool ieuclid = g.kind == gcEuclid;
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bool isphere = g.kind == gcSphere;
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bool ieuc_or_binary = ieuclid || (gi.flags & qBINARY);
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if(spatial_embedding == seProduct && !ieuclid) g = giProduct, g.sig[2] = og.sig[2];
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if(spatial_embedding == seProductH && ieuclid) g = giProductH;
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if(spatial_embedding == seProductS && ieuclid) g = giProductS;
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if(spatial_embedding == seLowerCurvature) g = (isphere ? giEuclid3 : giHyperb3);
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if(spatial_embedding == seMuchLowerCurvature) g = giHyperb3;
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if(spatial_embedding == seNil && ieuclid) g = giNil;
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if(spatial_embedding == seCliffordTorus && ieuclid) g = giSphere3;
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if(spatial_embedding == seSol && ieuc_or_binary) g = giSol;
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if(spatial_embedding == seNIH && ieuc_or_binary) g = giNIH;
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if(spatial_embedding == seSolN && ieuc_or_binary) g = giSolN;
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if(spatial_embedding == seSL2 && ieuclid) g = giSL2;
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if(spatial_embedding == seCylinderH && ieuclid) g = giHyperb3;
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if(spatial_embedding == seCylinderHE && ieuclid) g = giProductH;
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if(spatial_embedding == seCylinderHoro && ieuclid) g = giProductH;
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if(spatial_embedding == seCylinderNil && ieuclid) g = giNil;
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if(spatial_embedding == seCylinderSL2 && ieuclid) g = giSL2;
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g.gameplay_dimension = 2;
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}
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}
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EX void configure_clifford_torus() {
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#if CAP_RUG
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dynamicval<ld> dtessf(cgi.tessf, 1);
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rug::clifford_torus ct;
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if(hypot_d(2, ct.xh) < 1e-6 || hypot_d(2, ct.yh) < 1e-6) {
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euclid_embed_scale = TAU / 20.;
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euclid_embed_scale_y = 1;
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euclid_embed_rotate = 0;
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vid.depth = 45._deg - 1;
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vid.wall_height = 0.2;
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vid.eye = vid.wall_height / 2 - vid.depth;
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return;
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}
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euclid_embed_scale = TAU / hypot_d(2, ct.xh);
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euclid_embed_scale_y = TAU / hypot_d(2, ct.yh) / euclid_embed_scale;
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euclid_embed_rotate = atan2(ct.xh[1], ct.xh[0]) / degree;
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ld alpha = atan2(ct.xfactor, ct.yfactor);
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vid.depth = alpha - 1;
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vid.wall_height = min(1 / euclid_embed_scale_mean(), (90._deg - alpha) * 0.9);
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vid.eye = vid.wall_height / 2 - vid.depth;
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#endif
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}
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EX void configure_cylinder() {
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#if CAP_RUG
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dynamicval<ld> dtessf(cgi.tessf, 1);
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rug::clifford_torus ct;
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hyperpoint vec;
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if(sqhypot_d(2, ct.yh) > 1e-6) vec = ct.yh;
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else if(sqhypot_d(2, ct.xh) > 1e-6) vec = ct.xh;
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else vec = hyperpoint(10, 0, 0, 0);
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euclid_embed_scale = TAU / hypot_d(2, vec);
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euclid_embed_scale_y = 1;
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euclid_embed_rotate = atan2(vec[1], vec[0]) / degree;
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#endif
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}
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EX }
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#if HDR
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struct embedding_method {
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virtual ld center_z() { return 0; }
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virtual hyperpoint tile_center();
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virtual transmatrix intermediate_to_actual_translation(hyperpoint i) = 0;
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virtual hyperpoint intermediate_to_actual(hyperpoint i) { return intermediate_to_actual_translation(i) * tile_center(); }
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virtual hyperpoint actual_to_intermediate(hyperpoint a) = 0;
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virtual hyperpoint orthogonal_move(const hyperpoint& a, ld z);
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virtual transmatrix map_relative_push(hyperpoint h);
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virtual ld get_logical_z(hyperpoint a) { return (intermediate_to_logical_scaled * actual_to_intermediate(a))[2]; }
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virtual hyperpoint logical_to_actual(hyperpoint l) { return intermediate_to_actual(logical_to_intermediate * l); }
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virtual hyperpoint actual_to_logical(hyperpoint a) { return intermediate_to_logical * actual_to_intermediate(a); }
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virtual hyperpoint base_to_actual(hyperpoint h) = 0;
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virtual transmatrix base_to_actual(const transmatrix &T) = 0;
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virtual hyperpoint actual_to_base(hyperpoint h) = 0;
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virtual transmatrix actual_to_base(const transmatrix &T) = 0;
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virtual hyperpoint normalize_flat(hyperpoint a) { return flatten(normalize(a)); }
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virtual hyperpoint flatten(hyperpoint a);
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virtual void set_radar_transform();
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virtual transmatrix get_lsti() { return Id; }
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virtual transmatrix get_lti() { return logical_scaled_to_intermediate; }
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virtual hyperpoint base_to_logical(hyperpoint h) = 0;
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virtual hyperpoint logical_to_base(hyperpoint h) = 0;
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virtual ld anim_center_z() { return center_z(); }
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virtual hyperpoint anim_tile_center();
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virtual void logical_fix(transmatrix&) = 0;
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virtual ld height_limit(ld sign);
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virtual bool is_euc_in_product() { return false; }
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virtual bool is_product_embedding() { return false; }
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virtual bool is_euc_in_sl2() { return false; }
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virtual bool is_same_in_same() { return false; }
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virtual bool is_sph_in_low() { return false; }
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virtual bool is_hyp_in_solnih() { return false; }
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virtual bool is_euc_scalable() { return false; }
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virtual bool is_euc_in_hyp() { return false; }
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virtual bool is_euc_in_sph() { return false; }
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virtual bool is_euc_in_nil() { return false; }
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virtual bool is_euc_in_noniso() { return false; }
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virtual bool is_in_noniso() { return false; }
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virtual bool is_cylinder() { return false; }
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virtual bool no_spin() { return false; }
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/* convert the tangent space in logical coordinates to actual coordinates */
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transmatrix logical_to_intermediate;
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/* convert the tangent space in actual coordinates to logical coordinates */
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transmatrix intermediate_to_logical;
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/* convert the tangent space in logical coordinates to actual coordinates */
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transmatrix logical_scaled_to_intermediate;
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/* convert the tangent space in actual coordinates to logical coordinates */
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transmatrix intermediate_to_logical_scaled;
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void prepare_lta();
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void auto_configure();
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virtual ~embedding_method() {}
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/* should we break cylinder between M1 and M2 */
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virtual bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) { return false; }
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};
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#endif
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EX geometry_information *swapper;
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ld embedding_method::height_limit(ld sign) {
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if(sign > 0) {
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if(sol || nih) return 2.5;
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if(hyperbolic || sl2 || in_h2xe()) return 5;
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if(sphere || nil || in_s2xe()) return M_PI/2;
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return 100;
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}
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if(sign < 0) {
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if(center_z()) return -center_z();
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if(sol || nih) return -2.5;
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if(hyperbolic || sl2 || in_h2xe()) return -5;
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if(sphere || nil || in_s2xe()) return -M_PI/2;
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return -100;
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}
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return 0;
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}
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hyperpoint embedding_method::tile_center() {
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ld z = center_z();
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if(z == 0) return C0;
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return lzpush(z) * C0;
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}
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hyperpoint embedding_method::anim_tile_center() {
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ld z = anim_center_z();
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if(z == 0) return C0;
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return lzpush(z) * C0;
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}
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transmatrix embedding_method::map_relative_push(hyperpoint a) {
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auto i = actual_to_intermediate(a);
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return intermediate_to_actual_translation(i);
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}
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hyperpoint embedding_method::orthogonal_move(const hyperpoint& a, ld z) {
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auto i = actual_to_intermediate(a);
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auto l = intermediate_to_logical_scaled * i;
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l[2] += z;
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i = logical_scaled_to_intermediate * l;
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return intermediate_to_actual(i);
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}
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hyperpoint embedding_method::flatten(hyperpoint a) {
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auto i = actual_to_intermediate(a);
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auto l = intermediate_to_logical * i;
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l[2] = 0; i = logical_to_intermediate * l;
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return intermediate_to_actual(i);
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}
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/** dummy 'embedding method' used when no embedding is used (2D engine or 3D map) */
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struct emb_none : embedding_method {
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hyperpoint actual_to_intermediate(hyperpoint a) override {
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if(mhybrid) return base_to_logical(a);
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return a;
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}
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hyperpoint intermediate_to_actual(hyperpoint i) override {
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if(mhybrid) return logical_to_base(i);
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return i;
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}
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transmatrix intermediate_to_actual_translation(hyperpoint i) override {
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if(gproduct) i = intermediate_to_actual(i);
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return rgpushxto0(i);
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}
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hyperpoint flatten(hyperpoint a) override {
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if(gproduct || GDIM == 2) return a / exp(zlevel(a));
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return embedding_method::flatten(a);
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}
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hyperpoint normalize_flat(hyperpoint a) override { return gproduct ? flatten(a) : normalize(a); }
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transmatrix base_to_actual(const transmatrix& T) override { return T; }
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hyperpoint base_to_actual(hyperpoint h) override { return h; }
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transmatrix actual_to_base(const transmatrix& T) override { return T; }
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hyperpoint actual_to_base(hyperpoint h) override { return h; }
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hyperpoint orthogonal_move(const hyperpoint& h, ld z) override {
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if(GDIM == 2) return scale_point(h, geom3::scale_at_lev(z));
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if(gproduct) return scale_point(h, exp(z));
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if(sl2) return slr::translate(h) * cpush0(2, z);
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if(nil) return nisot::translate(h) * cpush0(2, z);
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if(translatable) return hpxy3(h[0], h[1], h[2] + z);
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/* copied from emb_same_in_same */
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ld u = 1;
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if(h[2]) z += asin_auto(h[2]), u /= cos_auto(asin_auto(h[2]));
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u *= cos_auto(z);
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return hpxy3(h[0] * u, h[1] * u, sinh(z));
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}
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hyperpoint base_to_logical(hyperpoint h) override {
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if(sn::in() || !bt::in())
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return h;
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#if CAP_BT
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if(bt::in() && !mproduct) return bt::minkowski_to_bt(h);
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#endif
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if(mproduct) {
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ld z = zlevel(h);
|
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h /= h[2];
|
|
h[2] = z;
|
|
}
|
|
if(sl2) {
|
|
ld z = atan2(h[2], h[3]);
|
|
h = slr::translate(h) * zpush0(-atan2(h[2], h[3]));
|
|
h[0] = h[0] / h[3]; h[1] = h[1] / h[3]; h[2] = z;
|
|
return h;
|
|
}
|
|
return h;
|
|
}
|
|
hyperpoint logical_to_base(hyperpoint h) override {
|
|
if(sn::in() || !bt::in())
|
|
return ultra_normalize(h);
|
|
#if CAP_BT
|
|
if(bt::in() && !mproduct)
|
|
return bt::bt_to_minkowski(h);
|
|
#endif
|
|
if(mproduct) {
|
|
ld z = h[2];
|
|
h[2] = 1;
|
|
flatten(h);
|
|
h *= exp(z);
|
|
}
|
|
if(sl2) {
|
|
ld z = h[2];
|
|
h[2] = 0; h[3] = 1; normalize(h);
|
|
h = slr::translate(h) * zpush0(z);
|
|
return h;
|
|
}
|
|
return h;
|
|
}
|
|
|
|
void logical_fix(transmatrix& T) override {
|
|
if(nonisotropic) {
|
|
hyperpoint h = tC0(T);
|
|
transmatrix rot = gpushxto0(h) * T;
|
|
fix_rotation(rot);
|
|
T = rgpushxto0(h) * rot;
|
|
}
|
|
else fixmatrix(T);
|
|
fixelliptic(T);
|
|
}
|
|
};
|
|
|
|
/** embeddings methods that are not emb_none */
|
|
|
|
struct emb_actual : embedding_method {
|
|
|
|
hyperpoint base_to_logical(hyperpoint h) override {
|
|
#if CAP_BT
|
|
if(bt::in()) {
|
|
auto h1 = bt::inverse_horopoint(h);
|
|
h1[2] = 0; h1[3] = 1;
|
|
return h1;
|
|
}
|
|
#endif
|
|
h /= h[2];
|
|
h[2] = 0; h[3] = 1;
|
|
return h;
|
|
}
|
|
|
|
hyperpoint logical_to_base(hyperpoint h) override {
|
|
#if CAP_BT
|
|
if(bt::in()) {
|
|
auto h1 = bt::get_horopoint(h);
|
|
h1[3] = 1;
|
|
return h1;
|
|
}
|
|
#endif
|
|
h[2] = 1; h = normalize(h);
|
|
h[3] = 1;
|
|
return h;
|
|
}
|
|
|
|
void logical_fix(transmatrix& T) override {
|
|
hyperpoint a = T * tile_center();
|
|
hyperpoint i0 = actual_to_intermediate(a);
|
|
auto l0 = intermediate_to_logical * i0;
|
|
auto l = l0; l[2] = 0;
|
|
auto i = logical_to_intermediate * l;
|
|
auto rot0= inverse(intermediate_to_actual_translation(i0)) * T ;
|
|
auto rot = intermediate_to_logical_scaled * rot0 * logical_scaled_to_intermediate;
|
|
ld alpha = atan2(rot[0][1], rot[0][0]);
|
|
T = intermediate_to_actual_translation(i) * spin(alpha);
|
|
fixelliptic(T);
|
|
}
|
|
};
|
|
|
|
/** embed in the 3D variant of the same geometry */
|
|
|
|
struct emb_same_in_same : emb_actual {
|
|
bool is_same_in_same() override { return true; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override { return rgpushxto0(logical_to_actual(i)); }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { return actual_to_logical(a); }
|
|
hyperpoint orthogonal_move(const hyperpoint& h, ld z) override {
|
|
if(euclid) { hyperpoint h1 = h; h1[2] += z; return h1; }
|
|
ld u = 1;
|
|
if(h[2]) z += asin_auto(h[2]), u /= cos_auto(asin_auto(h[2]));
|
|
u *= cos_auto(z);
|
|
return hpxy3(h[0] * u, h[1] * u, sinh(z));
|
|
}
|
|
transmatrix base_to_actual(const transmatrix &T0) override {
|
|
auto T = T0;
|
|
for(int i=0; i<4; i++) T[i][3] = T[i][2], T[i][2] = 0;
|
|
for(int i=0; i<4; i++) T[3][i] = T[2][i], T[i][2] = 0;
|
|
for(int i=0; i<4; i++) T[i][2] = T[2][i] = 0;
|
|
T[2][2] = 1;
|
|
return T;
|
|
}
|
|
transmatrix actual_to_base(const transmatrix &T0) override {
|
|
auto T = T0;
|
|
for(int i=0; i<4; i++) T[i][2] = T[i][3], T[i][3] = 0;
|
|
for(int i=0; i<4; i++) T[2][i] = T[3][i], T[3][i] = 0;
|
|
T[3][3] = 1;
|
|
if(MDIM == 3) fixmatrix(T); else IPF(fixmatrix(T));
|
|
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++) if(isnan(T[i][j])) return Id;
|
|
return T;
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override {
|
|
h[3] = h[2]; h[2] = 0;
|
|
return h;
|
|
}
|
|
hyperpoint actual_to_base(hyperpoint h) override {
|
|
h[2] = h[3]; h[3] = 0;
|
|
return h;
|
|
}
|
|
transmatrix map_relative_push(hyperpoint h) override {
|
|
ld z = asin_auto(h[2]);
|
|
ld u = 1 / cos_auto(z);
|
|
auto h1 = hpxy3(h[0] * u, h[1] * u, 0);
|
|
return rgpushxto0(h1) * zpush(z);
|
|
}
|
|
|
|
hyperpoint actual_to_logical(hyperpoint h) override {
|
|
if(euclid) { h[3] = 1; return h; }
|
|
ld z = asin_auto(h[2]);
|
|
ld u = 1 / cos_auto(z);
|
|
auto h1 = hpxy3(h[0] * u, h[1] * u, 0);
|
|
h1[2] = h1[3];
|
|
geom3::light_flip(true);
|
|
h1 = base_to_logical(h1);
|
|
geom3::light_flip(false);
|
|
h1[2] = z;
|
|
return h1;
|
|
}
|
|
|
|
hyperpoint logical_to_actual(hyperpoint h) override {
|
|
if(euclid) { h[3] = 1; return h; }
|
|
geom3::light_flip(true);
|
|
auto b = logical_to_base(h);
|
|
geom3::light_flip(false);
|
|
b[3] = b[2]; b[2] = 0;
|
|
return orthogonal_move(b, h[2]);
|
|
}
|
|
|
|
hyperpoint flatten(hyperpoint h) override {
|
|
ld z = asin_auto(h[2]);
|
|
ld u = 1 / cos_auto(z);
|
|
return hpxy3(h[0] * u, h[1] * u, 0);
|
|
}
|
|
|
|
void logical_fix(transmatrix& T) override {
|
|
// optimization
|
|
for(int i=0; i<4; i++) T[i][2] = T[2][i] = i == 2;
|
|
fixmatrix(T);
|
|
fixelliptic(T);
|
|
}
|
|
};
|
|
|
|
/** embed in the product geometry */
|
|
|
|
struct emb_product_embedding : emb_actual {
|
|
bool is_product_embedding() override { return true; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override { return rgpushxto0(logical_to_actual(i)); }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { return actual_to_logical(a); }
|
|
hyperpoint flatten(hyperpoint h) override { h /= exp(zlevel(h)); return h; }
|
|
hyperpoint orthogonal_move(const hyperpoint& h, ld z) override { return h * exp(z); }
|
|
transmatrix base_to_actual(const transmatrix &T) override { return T; }
|
|
transmatrix actual_to_base(const transmatrix &T0) override {
|
|
auto T = T0; fixmatrix(T);
|
|
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++) if(isnan(T[i][j])) return Id;
|
|
return T;
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override { return h; }
|
|
hyperpoint actual_to_base(hyperpoint h) override { return flatten(h); }
|
|
transmatrix map_relative_push(hyperpoint h) override { return rgpushxto0(h); }
|
|
|
|
hyperpoint actual_to_logical(hyperpoint h) override {
|
|
ld z = zlevel(h);
|
|
h /= exp(z);
|
|
h = base_to_logical(h);
|
|
h[2] = z;
|
|
return h;
|
|
}
|
|
|
|
hyperpoint logical_to_actual(hyperpoint h) override {
|
|
return logical_to_base(h) * exp(h[2]);
|
|
}
|
|
};
|
|
|
|
struct emb_euc_scalable : emb_actual {
|
|
bool is_euc_scalable() override { return true; }
|
|
transmatrix get_lti() override {
|
|
transmatrix lti = Id;
|
|
lti[0][0] *= geom3::euclid_embed_scale;
|
|
lti[1][1] *= geom3::euclid_embed_scale * geom3::euclid_embed_scale_y;
|
|
return logical_scaled_to_intermediate * cspin(0, 1, geom3::euclid_embed_rotate * degree) * lti;
|
|
}
|
|
};
|
|
|
|
/** embed Euclidean plane as horosphere */
|
|
|
|
struct emb_euc_in_hyp : emb_euc_scalable {
|
|
bool is_euc_in_hyp() override { return true; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { return deparabolic13(a); }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override { return parabolic13_at(i); }
|
|
transmatrix base_to_actual(const transmatrix &T) override {
|
|
geom3::light_flip(true);
|
|
hyperpoint mov = T * C02;
|
|
transmatrix U = gpushxto0(mov) * T;
|
|
mov = logical_to_intermediate * mov;
|
|
geom3::light_flip(false);
|
|
for(int i=0; i<4; i++) U[i][3] = U[3][i] = i == 3;
|
|
return parabolic13(mov[0], mov[1]) * U;
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override {
|
|
h = logical_to_intermediate * h;
|
|
h[3] = h[2]; h[2] = 0; return parabolic13(h[0], h[1]) * C0;
|
|
}
|
|
hyperpoint actual_to_base(hyperpoint h) override {
|
|
hyperpoint h1 = deparabolic13(h); h1[2] = 1;
|
|
return intermediate_to_logical * h1;
|
|
}
|
|
transmatrix actual_to_base(const transmatrix& T) override { hyperpoint h = deparabolic13(T * C0); return eupush(h[0], h[1]); }
|
|
ld anim_center_z() override { return vid.depth; }
|
|
};
|
|
|
|
/** sphere into a isotropic space of higher curvature */
|
|
|
|
struct emb_sphere_in_low : emb_actual {
|
|
bool is_sph_in_low() override { return true; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return map_relative_push(logical_to_actual(i)) * zpush(-1);
|
|
}
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { return actual_to_logical(a); }
|
|
ld center_z() override { return 1; }
|
|
transmatrix map_relative_push(hyperpoint a) override {
|
|
ld z = hdist0(a);
|
|
geom3::light_flip(true);
|
|
auto h1 = normalize(a);
|
|
transmatrix T = rgpushxto0(h1);
|
|
geom3::light_flip(false);
|
|
return T * zpush(z);
|
|
}
|
|
transmatrix base_to_actual(const transmatrix &T0) override {
|
|
auto T = T0;
|
|
for(int i=0; i<4; i++) T[i][3] = T[3][i] = i == 3;
|
|
return T;
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override {
|
|
if(euclid) h[3] = 1;
|
|
else h *= sinh(1), h[3] = cosh(1);
|
|
return h;
|
|
}
|
|
hyperpoint actual_to_base(hyperpoint h) override { return h; }
|
|
transmatrix actual_to_base(const transmatrix& T) override { return T; }
|
|
ld get_logical_z(hyperpoint a) override { return hdist0(a) - 1; }
|
|
hyperpoint flatten(hyperpoint a) override {
|
|
ld d = hdist0(a);
|
|
if(d == 0) return a;
|
|
a *= sin_auto(1) / sin_auto(d);
|
|
a[3] = cos_auto(1);
|
|
return a;
|
|
}
|
|
hyperpoint orthogonal_move(const hyperpoint& h, ld z) override {
|
|
ld z0 = hdist0(h);
|
|
ld f = sin_auto(z0 + z) / sin_auto(z0);
|
|
hyperpoint hf = h * f;
|
|
hf[3] = cos_auto(z0 + z);
|
|
return hf;
|
|
}
|
|
hyperpoint logical_to_actual(hyperpoint h) override {
|
|
auto z = h[2];
|
|
h[2] = 1;
|
|
geom3::light_flip(true);
|
|
h = normalize(h);
|
|
geom3::light_flip(false);
|
|
h *= sin_auto(1 + z);
|
|
h[3] = cos_auto(1 + z);
|
|
return h;
|
|
}
|
|
hyperpoint actual_to_logical(hyperpoint h) override {
|
|
ld z = get_logical_z(h);
|
|
geom3::light_flip(true);
|
|
h = kleinize(h);
|
|
geom3::light_flip(false);
|
|
h[2] = z; h[3] = 1;
|
|
return h;
|
|
}
|
|
|
|
void logical_fix(transmatrix& T) override {
|
|
fix4(T);
|
|
fixmatrix(T);
|
|
fixelliptic(T);
|
|
}
|
|
};
|
|
|
|
/** abstract class for embeddings of Euclidean plane; these embeddings are not isotropic */
|
|
|
|
struct emb_euclid_noniso : emb_euc_scalable {
|
|
bool is_euc_in_noniso() override { return true; }
|
|
bool is_in_noniso() override { return true; }
|
|
transmatrix base_to_actual(const transmatrix &T) override {
|
|
auto T0 = T;
|
|
hyperpoint h = get_column(T0, 2);
|
|
h[2] = 0; h[3] = 1;
|
|
return intermediate_to_actual_translation( logical_to_intermediate * h);
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override {
|
|
h[2] = 0; h[3] = 1;
|
|
return intermediate_to_actual_translation( logical_to_intermediate * h ) * tile_center();
|
|
}
|
|
hyperpoint actual_to_base(hyperpoint h) override {
|
|
hyperpoint h1 = intermediate_to_logical * actual_to_intermediate(h);
|
|
h1[2] = 1; h1[3] = 0;
|
|
return h1;
|
|
}
|
|
transmatrix actual_to_base(const transmatrix& T) override { hyperpoint h = actual_to_base(T * tile_center()); return eupush(h[0], h[1]); }
|
|
};
|
|
|
|
struct emb_euc_in_product : emb_euclid_noniso {
|
|
bool is_euc_in_product() override { return true; }
|
|
bool no_spin() override { return true; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld bz = zlevel(a);
|
|
auto h1 = a / exp(bz);
|
|
ld by = asin_auto(h1[1]);
|
|
ld bx = atan2_auto(h1[0], h1[2]);
|
|
return hyperpoint(bx, by, bz, 1);
|
|
}
|
|
transmatrix get_lsti() override { return cspin90(2, 1); }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return zpush(i[2]) * xpush(i[0]) * ypush(i[1]);
|
|
}
|
|
};
|
|
|
|
struct emb_euc_in_sl2 : emb_euclid_noniso {
|
|
|
|
transmatrix esl2_zpush(ld z) { return cspin(2, 3, z) * cspin(0, 1, z); }
|
|
|
|
hyperpoint intermediate_to_actual(hyperpoint i) override {
|
|
return esl2_zpush(i[2]) * xpush(i[0]) * ypush0(i[1]);
|
|
}
|
|
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return esl2_zpush(i[2]) * xpush(i[0]) * ypush(i[1]);
|
|
}
|
|
|
|
hyperpoint actual_to_intermediate(hyperpoint h) override {
|
|
ld a1 = (h[0] * h[3] - h[1] * h[2]) / (-h[2] * h[2] - h[1] * h[1] -h[0] * h[0] - h[3] * h[3]);
|
|
// a1 is S*sqrt(1+S*S) / (1+2*S*S), where S = sinh(-x) and C = cosh(-x); U is S*S
|
|
ld a = a1 * a1;
|
|
ld b = 4 * a - 1;
|
|
ld U = sqrt(.25 - a/b) - .5;
|
|
ld S = sqrt(U) * (a1 > 0 ? 1 : -1);
|
|
ld x = -asinh(S);
|
|
h = lorentz(0, 3, -x) * lorentz(1, 2, x) * h;
|
|
ld y = h[3]*h[3] > h[2]*h[2] ? atanh(h[1] / h[3]) : atanh(h[0] / h[2]);
|
|
h = lorentz(0, 2, -y) * lorentz(1, 3, -y) * h;
|
|
ld z = atan2(h[2], h[3]);
|
|
return hyperpoint(x, y, z, 0);
|
|
}
|
|
|
|
bool is_euc_in_sl2() override { return true; }
|
|
bool no_spin() override { return true; }
|
|
transmatrix get_lsti() override { return cspin90(2, 1); }
|
|
};
|
|
|
|
bool break_dims(const shiftmatrix& M1, const shiftmatrix& M2, int i, int j) {
|
|
transmatrix uM1 = current_display->radar_transform * unshift(M1);
|
|
transmatrix uM2 = current_display->radar_transform * unshift(M2);
|
|
return uM1[j][j] < 0 && uM2[j][j] < 0 && uM1[i][j] * uM2[i][j] < 0;
|
|
}
|
|
|
|
/* for both seCylinderH and seCylinderE. Possibly actually works for CliffordTorus too */
|
|
struct emb_euc_cylinder : emb_euclid_noniso {
|
|
bool is_cylinder() override { return true; }
|
|
ld center_z() override { return 1; }
|
|
transmatrix get_lsti() override { return cspin90(0, 1); }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld z0 = asin_auto(hypot(a[1], a[2]));
|
|
ld x0 = a[0];
|
|
if(z0 == 0) return hyperpoint(x0, 0, 0, 1);
|
|
x0 = asin_auto(x0 / cos_auto(z0));
|
|
ld y0 = z0 ? atan2(a[1], a[2]) : 0;
|
|
return point31(x0, y0, z0-1);
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return xpush(i[0]) * cspin(1, 2, i[1]) * zpush(i[2]);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return break_dims(M1, M2, 1, 2); }
|
|
};
|
|
|
|
struct emb_euc_cylinder_he : emb_euc_cylinder {
|
|
bool no_spin() override { return true; }
|
|
transmatrix get_lsti() override { return cspin90(0, 2) * cspin90(0, 1); }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld z0 = zlevel(a);
|
|
a /= exp(z0);
|
|
ld y0 = atan2(a[1], a[0]);
|
|
ld x0 = asin_auto(hypot(a[0], a[1]));
|
|
return hyperpoint(x0-1, y0, z0, 1);
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return zpush(i[2]) * cspin(1, 0, i[1]) * xpush(i[0]);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return break_dims(M1, M2, 1, 0); }
|
|
};
|
|
|
|
struct emb_euc_cylinder_twisted : emb_euc_cylinder {
|
|
transmatrix get_lsti() override { return cspin90(0, 2) * cspin90(0, 1); }
|
|
transmatrix get_lti() override {
|
|
ld depth = 0; // for now?
|
|
ld alpha = nil ? (1 + depth) / 2. : sinh(1 + depth) / 2.;
|
|
ld c = pow(1 + alpha * alpha, -0.5);
|
|
transmatrix U = Id;
|
|
U[1][1] = (alpha*alpha+1) * c;
|
|
U[0][1] = alpha * c;
|
|
return logical_scaled_to_intermediate * U * intermediate_to_logical_scaled * emb_euc_cylinder::get_lti();
|
|
}
|
|
};
|
|
|
|
struct emb_euc_cylinder_nil : emb_euc_cylinder_twisted {
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld y0 = atan2(a[1], a[0]);
|
|
ld x0 = hypot(a[0], a[1]);
|
|
return hyperpoint(x0-1, y0, a[2], 1);
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return zpush(i[2]) * cspin(1, 0, i[1]) * xpush(i[0]);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return break_dims(M1, M2, 1, 0); }
|
|
};
|
|
|
|
struct emb_euc_cylinder_horo : emb_euc_cylinder {
|
|
ld center_z() override { return 0; }
|
|
bool no_spin() override { return true; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld z0 = zlevel(a);
|
|
a /= exp(z0);
|
|
auto hy = deparabolic13(a);
|
|
hy[2] = z0;
|
|
return hy;
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return zpush(i[2]) * parabolic1(i[1]) * xpush(i[0]);
|
|
}
|
|
transmatrix get_lsti() override {
|
|
return cspin90(0, 2);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return false; }
|
|
};
|
|
|
|
struct emb_euc_cylinder_sl2 : emb_euc_cylinder_twisted {
|
|
bool no_spin() override { return true; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
hyperpoint i = point31(0, 0, 0);
|
|
i[2] = atan2(a[2], a[3]);
|
|
a = cspin(1, 0, i[2]) * cspin(3, 2, i[2]) * a;
|
|
i[1] = (a[0] || a[1]) ? -atan2(a[1], a[0]) : 0;
|
|
a = cspin(1, 0, i[1]) * a;
|
|
i[0] = asinh(a[0])-1;
|
|
return i;
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return cspin(2, 3, i[2]) * cspin(0, 1, i[2] + i[1]) * xpush(i[0]);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return break_dims(M1, M2, 0, 1); }
|
|
};
|
|
|
|
/** Clifford torus */
|
|
struct emb_euc_in_sph : emb_euclid_noniso {
|
|
bool is_euc_in_sph() override { return true; }
|
|
ld center_z() override { return 1; }
|
|
// ld height_limit(ld sign) override { return sign < 0 ? 0 : 90._deg; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
ld tx = hypot(a[0], a[2]);
|
|
ld ty = hypot(a[1], a[3]);
|
|
ld x0 = atan2(a[0], a[2]);
|
|
ld y0 = atan2(a[1], a[3]);
|
|
ld z0 = atan2(tx, ty);
|
|
return hyperpoint(x0, y0, z0-1, 1);
|
|
}
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
return cspin(0, 2, i[0]) * cspin(1, 3, i[1]) * cspin(2, 3, i[2]);
|
|
}
|
|
bool break_cylinder(const shiftmatrix& M1, const shiftmatrix& M2) override { return break_dims(M1, M2, 0, 2) || break_dims(M1, M2, 1, 3); }
|
|
};
|
|
|
|
/* todo model change */
|
|
struct emb_euc_in_nil : emb_euclid_noniso {
|
|
bool is_euc_in_nil() override { return true; }
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { a[2] -= a[0] * a[1] / 2; return a; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override { i[2] += i[0] * i[1] / 2; return rgpushxto0(i); }
|
|
transmatrix get_lsti() override { return cspin90(2, 1); }
|
|
};
|
|
|
|
struct emb_euc_in_solnih : emb_euclid_noniso {
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override { return a; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override { return rgpushxto0(i); }
|
|
};
|
|
|
|
struct emb_hyp_in_solnih : emb_actual {
|
|
bool is_hyp_in_solnih() override { return true; }
|
|
bool is_in_noniso() override { return true; }
|
|
transmatrix intermediate_to_actual_translation(hyperpoint i) override {
|
|
if(cgclass == gcSol) i[0] *= exp(-i[2]);
|
|
if(cgclass == gcSolN) i[0] *= pow(2, -i[2]);
|
|
if(cgclass == gcNIH) i[0] *= pow(2, i[2]);
|
|
return rgpushxto0(i);
|
|
}
|
|
hyperpoint actual_to_intermediate(hyperpoint a) override {
|
|
if(cgclass == gcSol) a[0] *= exp(a[2]);
|
|
if(cgclass == gcSolN) a[0] *= pow(2, a[2]);
|
|
if(cgclass == gcNIH) a[0] *= pow(2, -a[2]);
|
|
return a;
|
|
}
|
|
transmatrix base_to_actual(const transmatrix &T) override {
|
|
auto T1 = T;
|
|
auto h = get_column(T1, 2);
|
|
return rgpushxto0(base_to_actual(h));
|
|
}
|
|
hyperpoint base_to_actual(hyperpoint h) override {
|
|
// copied from deparabolic13
|
|
h /= (1 + h[2]);
|
|
h[0] -= 1;
|
|
h /= sqhypot_d(2, h);
|
|
h[0] += .5;
|
|
ld hx = log(2) + log(-h[0]);
|
|
if(cgclass == gcNIH) hx /= log(3);
|
|
if(cgclass == gcSolN) hx /= log(3);
|
|
ld hy = h[1] * 2;
|
|
return point31(0, -hy, hx);
|
|
}
|
|
transmatrix actual_to_base(const transmatrix& T) override {
|
|
hyperpoint h = T * C0;
|
|
auto f = geom3::flipped;
|
|
geom3::light_flip(true);
|
|
transmatrix b = parabolic1(h[1]) * xpush(h[2]);
|
|
geom3::light_flip(f);
|
|
return b;
|
|
}
|
|
hyperpoint actual_to_base(hyperpoint h) override {
|
|
auto f = geom3::flipped;
|
|
geom3::light_flip(true);
|
|
hyperpoint b = parabolic1(h[1]) * xpush0(h[2]);
|
|
geom3::light_flip(f);
|
|
return b;
|
|
}
|
|
transmatrix get_lsti() override { return cspin90(0, 1) * cspin90(1, 2) * cspin90(0, 1); }
|
|
hyperpoint orthogonal_move(const hyperpoint& a, ld z) override { return nisot::translate(a) * cpush0(0, z); }
|
|
};
|
|
|
|
/* the remaining methods */
|
|
/*=======================*/
|
|
|
|
void embedding_method::prepare_lta() {
|
|
bool b = geom3::flipped;
|
|
if(b) geom3::light_flip(false);
|
|
|
|
logical_scaled_to_intermediate = get_lsti();
|
|
intermediate_to_logical_scaled = inverse(logical_scaled_to_intermediate);
|
|
logical_to_intermediate = get_lti();
|
|
intermediate_to_logical = inverse(logical_to_intermediate);
|
|
if(MDIM == 3 && MAXMDIM == 4) {
|
|
// just in case
|
|
for(int i=0; i<4; i++)
|
|
intermediate_to_logical_scaled[i][3] = intermediate_to_logical_scaled[3][i] = intermediate_to_logical[3][i] = intermediate_to_logical[i][3] = i == 3;
|
|
}
|
|
if(b) geom3::light_flip(true);
|
|
}
|
|
|
|
/** pick the embedding_method for the current setting */
|
|
EX unique_ptr<embedding_method> make_embed() {
|
|
|
|
embedding_method *emb1;
|
|
using namespace geom3;
|
|
|
|
if(!embedded_plane)
|
|
emb1 = new emb_none;
|
|
else if(any_cylinder(spatial_embedding) && mgclass() == gcEuclid)
|
|
emb1 = spatial_embedding == seCylinderHE ? new emb_euc_cylinder_he :
|
|
spatial_embedding == seCylinderHoro ? new emb_euc_cylinder_horo :
|
|
spatial_embedding == seCylinderNil ? new emb_euc_cylinder_nil :
|
|
spatial_embedding == seCylinderSL2 ? new emb_euc_cylinder_sl2 :
|
|
new emb_euc_cylinder;
|
|
else if(mgclass() == ggclass())
|
|
emb1 = new emb_same_in_same;
|
|
else if(mgclass() == gcSphere && among(ggclass(), gcHyperbolic, gcEuclid))
|
|
emb1 = new emb_sphere_in_low;
|
|
else if(mgclass() == gcEuclid && ggclass() == gcSphere)
|
|
emb1 = new emb_euc_in_sph;
|
|
else if(mgclass() == gcEuclid && ggclass() == gcSL2)
|
|
emb1 = new emb_euc_in_sl2;
|
|
else if(mgclass() == gcHyperbolic && among(ggclass(), gcSol, gcNIH, gcSolN))
|
|
emb1 = new emb_hyp_in_solnih;
|
|
else if(mgclass() == gcEuclid && ggclass() == gcProduct)
|
|
emb1 = new emb_euc_in_product;
|
|
else if(ggclass() == gcProduct)
|
|
emb1 = new emb_product_embedding;
|
|
else if(mgclass() == gcEuclid && ggclass() == gcNil)
|
|
emb1 = new emb_euc_in_nil;
|
|
else if(mgclass() == gcEuclid && ggclass() == gcHyperbolic)
|
|
emb1 = new emb_euc_in_hyp;
|
|
else if(mgclass() == gcEuclid && among(ggclass(), gcSol, gcNIH, gcSolN))
|
|
emb1 = new emb_euc_in_solnih;
|
|
else
|
|
throw hr_exception("unknown embedding");
|
|
|
|
unique_ptr<embedding_method> emb(emb1);
|
|
|
|
emb->prepare_lta();
|
|
return emb;
|
|
}
|
|
|
|
EX hyperpoint orthogonal_move(hyperpoint h, ld z ) { return cgi.emb->orthogonal_move(h, z); }
|
|
|
|
EX transmatrix unswap_spin(transmatrix T) {
|
|
return cgi.emb->intermediate_to_logical_scaled * T * cgi.emb->logical_scaled_to_intermediate;
|
|
}
|
|
|
|
/** rotate by alpha degrees in the XY plane */
|
|
EX transmatrix spin(ld alpha) {
|
|
#if MAXMDIM == 3
|
|
return cspin(0, 1, alpha);
|
|
#else
|
|
if(cgi.emb->no_spin()) return Id;
|
|
return cgi.emb->logical_scaled_to_intermediate * cspin(0, 1, alpha) * cgi.emb->intermediate_to_logical_scaled;
|
|
#endif
|
|
}
|
|
|
|
/** rotate by 90 degrees in the XY plane */
|
|
EX transmatrix spin90() {
|
|
#if MAXMDIM == 3
|
|
return cspin90(0, 1);
|
|
#else
|
|
if(cgi.emb->no_spin()) return Id;
|
|
return cgi.emb->logical_scaled_to_intermediate * cspin90(0, 1) * cgi.emb->intermediate_to_logical_scaled;
|
|
#endif
|
|
}
|
|
|
|
/** rotate by 180 degrees in the XY plane */
|
|
EX transmatrix spin180() {
|
|
#if MAXMDIM == 3
|
|
return cspin180(0, 1);
|
|
#else
|
|
if(cgi.emb->no_spin()) return Id;
|
|
return cgi.emb->logical_scaled_to_intermediate * cspin180(0, 1) * cgi.emb->intermediate_to_logical_scaled;
|
|
#endif
|
|
}
|
|
|
|
/** rotate by 270 degrees in the XY plane */
|
|
EX transmatrix spin270() {
|
|
#if MAXMDIM == 3
|
|
return cspin90(1, 0);
|
|
#else
|
|
if(cgi.emb->no_spin()) return Id;
|
|
return cgi.emb->logical_scaled_to_intermediate * cspin90(1, 0) * cgi.emb->intermediate_to_logical_scaled;
|
|
#endif
|
|
}
|
|
|
|
EX transmatrix lzpush(ld z) {
|
|
#if MAXMDIM >= 4
|
|
auto <i = cgi.emb->logical_scaled_to_intermediate;
|
|
if(lti[0][2]) return cpush(0, lti[0][2] * z);
|
|
if(lti[1][2]) return cpush(1, lti[1][2] * z);
|
|
#endif
|
|
return cpush(2, z);
|
|
}
|
|
|
|
EX transmatrix lxpush(ld alpha) {
|
|
#if MAXMDIM >= 4
|
|
if(embedded_plane) {
|
|
geom3::light_flip(true);
|
|
auto t = cpush(0, alpha);
|
|
geom3::light_flip(false);
|
|
return cgi.emb->base_to_actual(t);
|
|
}
|
|
#endif
|
|
return cpush(0, alpha);
|
|
}
|
|
|
|
EX hyperpoint lxpush0(ld x) { return lxpush(x) * tile_center(); }
|
|
|
|
EX transmatrix lspintox(const hyperpoint& H) {
|
|
if(cgi.emb->no_spin()) return Id;
|
|
if(embedded_plane) {
|
|
hyperpoint H1 = cgi.emb->intermediate_to_logical_scaled * H;
|
|
return cgi.emb->logical_scaled_to_intermediate * spintoc(H1, 0, 1) * cgi.emb->intermediate_to_logical_scaled;
|
|
}
|
|
if(WDIM == 2 || gproduct) return spintoc(H, 0, 1);
|
|
transmatrix T1 = spintoc(H, 0, 1);
|
|
return spintoc(T1*H, 0, 2) * T1;
|
|
}
|
|
|
|
EX transmatrix lrspintox(const hyperpoint& H) {
|
|
if(cgi.emb->no_spin()) return Id;
|
|
if(embedded_plane) {
|
|
hyperpoint H1 = cgi.emb->intermediate_to_logical_scaled * H;
|
|
return cgi.emb->logical_scaled_to_intermediate * rspintoc(H1, 0, 1) * cgi.emb->intermediate_to_logical_scaled;
|
|
}
|
|
if(WDIM == 2 || gproduct) return rspintoc(H, 0, 1);
|
|
transmatrix T1 = spintoc(H, 0, 1);
|
|
return rspintoc(H, 0, 1) * rspintoc(T1*H, 0, 2);
|
|
}
|
|
|
|
/** tangent vector in logical direction Z */
|
|
EX hyperpoint lztangent(ld z) {
|
|
return cgi.emb->logical_to_intermediate * ctangent(2, z);
|
|
}
|
|
|
|
EX hyperpoint tile_center() { return cgi.emb->tile_center(); }
|
|
|
|
EX hyperpoint lspinpush0(ld alpha, ld x) {
|
|
bool f = embedded_plane;
|
|
if(f) geom3::light_flip(true);
|
|
if(embedded_plane) throw hr_exception("still embedded plane");
|
|
hyperpoint h = xspinpush0(alpha, x);
|
|
if(f) geom3::light_flip(false);
|
|
if(f) return cgi.emb->base_to_actual(h);
|
|
return h;
|
|
}
|
|
|
|
EX hyperpoint xspinpush0(ld alpha, ld x) {
|
|
if(embedded_plane) return lspinpush0(alpha, x);
|
|
if(sl2) return slr::polar(x, -alpha, 0);
|
|
hyperpoint h = Hypc;
|
|
h[LDIM] = cos_auto(x);
|
|
h[0] = sin_auto(x) * cos(alpha);
|
|
h[1] = sin_auto(x) * -sin(alpha);
|
|
return h;
|
|
}
|
|
|
|
EX transmatrix xspinpush(ld dir, ld dist) {
|
|
if(embedded_plane) {
|
|
geom3::light_flip(true);
|
|
transmatrix T = cspin(0, 1, dir) * xpush(dist) * cspin(0, 1, -dir);
|
|
geom3::light_flip(false);
|
|
return cgi.emb->base_to_actual(T);
|
|
}
|
|
else if(euclid)
|
|
return eupush(cos(dir) * dist, -sin(dir) * dist);
|
|
else
|
|
return spin(dir) * xpush(dist) * spin(-dir);
|
|
}
|
|
|
|
EX const transmatrix& lmirror() {
|
|
if(cgi.emb->is_euc_in_product()) return Id;
|
|
if(cgi.emb->is_cylinder() && nil) return Id;
|
|
if(cgi.emb->logical_to_intermediate[2][1]) return MirrorZ;
|
|
if(cgi.emb->is_hyp_in_solnih()) return MirrorY;
|
|
return Mirror;
|
|
}
|
|
|
|
void embedding_method::set_radar_transform() {
|
|
auto& rt = current_display->radar_transform;
|
|
auto& rtp = current_display->radar_transform_post;
|
|
|
|
if(!embedded_plane) { rt = rtp = Id; return; }
|
|
transmatrix U = actual_view_transform * View;
|
|
auto a = inverse(U) * C0;
|
|
auto l = actual_to_intermediate(a);
|
|
l = intermediate_to_logical * l;
|
|
auto l0 = l;
|
|
l[2] = 0;
|
|
l = logical_to_intermediate * l;
|
|
rt = inverse(intermediate_to_actual_translation(l)) * inverse(U);
|
|
transmatrix T = View * intermediate_to_actual_translation(logical_to_intermediate * l0);
|
|
if(gproduct) T = NLP * T;
|
|
T = intermediate_to_logical_scaled * T * logical_scaled_to_intermediate;
|
|
if(cgi.emb->is_euc_in_noniso()) T = cspin(1, 0, geom3::euclid_embed_rotate * degree) * T;
|
|
if(cgi.emb->is_hyp_in_solnih()) T = T * MirrorY;
|
|
rtp = cspin(0, 1, atan2(T[0][1], T[0][0]));
|
|
if(cgi.emb->is_hyp_in_solnih()) rtp = MirrorX * cspin90(0, 1) * rtp;
|
|
}
|
|
|
|
EX void swapmatrix(transmatrix& T) {
|
|
if(geom3::swap_direction == +1) T = cgi.emb->base_to_actual(T);
|
|
if(geom3::swap_direction == -1) T = cgi.emb->actual_to_base(T);
|
|
}
|
|
|
|
EX void swappoint(hyperpoint& h) {
|
|
if(geom3::swap_direction == +1) h = cgi.emb->base_to_actual(h);
|
|
if(geom3::swap_direction == -1) h = cgi.emb->actual_to_base(h);
|
|
}
|
|
|
|
struct embedded_matrix_data {
|
|
transmatrix saved;
|
|
hyperpoint logical_coordinates;
|
|
transmatrix rotation;
|
|
ld old_height;
|
|
};
|
|
|
|
map<transmatrix*, embedded_matrix_data> mdata;
|
|
|
|
EX void swapmatrix_iview(transmatrix& ori, transmatrix& V) {
|
|
indenter id(2);
|
|
if(geom3::swap_direction == -1) {
|
|
auto& data = mdata[&V];
|
|
data.logical_coordinates = cgi.emb->intermediate_to_logical * cgi.emb->actual_to_intermediate(V*C0);
|
|
|
|
auto tl = cgi.emb->intermediate_to_actual_translation(cgi.emb->logical_to_intermediate * data.logical_coordinates);
|
|
auto itl = inverse(tl * lzpush(cgi.emb->center_z()));
|
|
data.rotation = itl * V;
|
|
|
|
auto& lc = data.logical_coordinates;
|
|
data.logical_coordinates[2] = ilerp(cgi.FLOOR, cgi.WALL, lc[2]);
|
|
|
|
if(nisot::local_perspective_used) data.rotation = data.rotation * ori;
|
|
swapmatrix(V);
|
|
|
|
data.rotation = cgi.emb->intermediate_to_logical_scaled * data.rotation;
|
|
data.saved = V;
|
|
data.old_height = vid.wall_height;
|
|
}
|
|
if(geom3::swap_direction == 1) {
|
|
if(!mdata.count(&V)) { swapmatrix(V); ori = Id; return; }
|
|
auto& data = mdata[&V];
|
|
if(!eqmatrix(data.saved, V)) { swapmatrix(V); ori = Id; return; }
|
|
auto lc = data.logical_coordinates;
|
|
lc[2] = lerp(cgi.FLOOR, cgi.WALL, lc[2]) + cgi.emb->center_z();
|
|
V = cgi.emb->intermediate_to_actual_translation( cgi.emb->logical_to_intermediate * lc );
|
|
ori = Id;
|
|
auto rot = data.rotation;
|
|
rot = cgi.emb->logical_scaled_to_intermediate * rot;
|
|
if(nisot::local_perspective_used) ori = ori * rot;
|
|
else V = V * rot;
|
|
if(vid.wall_height * data.old_height < 0) V = MirrorY * V;
|
|
}
|
|
}
|
|
|
|
EX void swapmatrix_view(transmatrix& lp, transmatrix& V) {
|
|
if(!geom3::swap_direction) return;
|
|
if(geom3::swap_direction == +1) fix4(V);
|
|
V = inverse(V);
|
|
lp = inverse(lp);
|
|
swapmatrix_iview(lp, V);
|
|
if(geom3::swap_direction == -1) fix4(V);
|
|
V = inverse(V);
|
|
lp = inverse(lp);
|
|
}
|
|
|
|
void embedding_method::auto_configure() {
|
|
using namespace geom3;
|
|
ld ms = min<ld>(cgi.scalefactor, 1);
|
|
vid.depth = ms;
|
|
vid.wall_height = 1.5 * ms;
|
|
if(sphere && msphere) {
|
|
vid.depth = 30 * degree;
|
|
vid.wall_height = 60 * degree;
|
|
}
|
|
vid.human_wall_ratio = 0.8;
|
|
if(mgclass() == gcEuclid && allowIncreasedSight() && vid.use_smart_range == 0) {
|
|
genrange_bonus = gamerange_bonus = sightrange_bonus = cgi.base_distlimit * 3/2;
|
|
}
|
|
vid.camera = 0;
|
|
vid.eye = 0;
|
|
if(is_sph_in_low() || is_cylinder()) {
|
|
vid.depth = 0;
|
|
vid.wall_height = -1;
|
|
vid.eye = -0.5;
|
|
if(inverted_embedding) {
|
|
vid.wall_height = is_cylinder() ? 0.6 : 1.4;
|
|
vid.eye = is_cylinder() ? 0.5 : 0.2;
|
|
vid.depth = is_cylinder() ? 0 : 0.5;
|
|
}
|
|
}
|
|
if(supports_flat() && flat_embedding) {
|
|
vid.eye += vid.depth / 2;
|
|
vid.depth = 0;
|
|
}
|
|
if(spatial_embedding == seDefault && !flat_embedding && inverted_embedding) {
|
|
vid.eye += vid.depth * 1.5;
|
|
vid.depth *= -1;
|
|
}
|
|
if((is_euc_in_hyp() || is_euc_in_noniso()) && inverted_embedding && !is_cylinder()) {
|
|
vid.wall_height *= -1;
|
|
vid.eye = -2 * vid.depth;
|
|
}
|
|
if(is_euc_in_nil() || is_euc_in_sl2()) {
|
|
vid.depth = 0;
|
|
vid.eye = vid.wall_height / 2;
|
|
}
|
|
if(is_euc_in_hyp() && spatial_embedding == seMuchLowerCurvature) {
|
|
vid.eye = inverted_embedding ? -vid.depth : vid.depth;
|
|
vid.depth = 0;
|
|
}
|
|
if(msphere && spatial_embedding == seProduct) {
|
|
vid.depth = 0;
|
|
vid.wall_height = 2;
|
|
vid.eye = 2;
|
|
}
|
|
if(pmodel == mdDisk) pmodel = nonisotropic ? mdGeodesic : mdPerspective;
|
|
if(cgflags & qIDEAL && vid.texture_step < 32)
|
|
vid.texture_step = 32;
|
|
#if CAP_RACING
|
|
racing::player_relative = true;
|
|
#endif
|
|
if(hyperbolic && is_same_in_same() && spatial_embedding == seLowerCurvature) {
|
|
vid.eye += vid.depth;
|
|
vid.depth *= 2;
|
|
if(inverted_embedding) {
|
|
vid.eye = 1;
|
|
vid.depth *= -1;
|
|
vid.wall_height *= -1;
|
|
}
|
|
}
|
|
if(hyperbolic && is_same_in_same() && spatial_embedding == seMuchLowerCurvature) {
|
|
vid.eye += vid.depth;
|
|
vid.depth *= 3;
|
|
if(inverted_embedding) {
|
|
vid.eye = 2;
|
|
vid.depth *= -1;
|
|
vid.wall_height *= -1;
|
|
}
|
|
}
|
|
if(spatial_embedding == seCliffordTorus) configure_clifford_torus();
|
|
if(spatial_embedding == seProductS) configure_cylinder();
|
|
if(spatial_embedding == seCylinderE) configure_cylinder();
|
|
if(spatial_embedding == seCylinderH) configure_cylinder();
|
|
if(spatial_embedding == seCylinderHE) configure_cylinder();
|
|
if(spatial_embedding == seCylinderSL2) configure_cylinder();
|
|
if(spatial_embedding == seCylinderNil) configure_cylinder();
|
|
}
|
|
|
|
EX void invoke_embed(geom3::eSpatialEmbedding se) {
|
|
#if MAXMDIM >= 4
|
|
if(GDIM == 3) { if(geom3::auto_configure) geom3::switch_fpp(); else geom3::switch_always3(); }
|
|
if(in_tpp()) geom3::switch_tpp();
|
|
if(se != geom3::seNone) {
|
|
geom3::spatial_embedding = se;
|
|
if(geom3::auto_configure) geom3::switch_fpp(); else geom3::switch_always3();
|
|
delete_sky();
|
|
if(vid.usingGL) resetGL();
|
|
}
|
|
#endif
|
|
}
|
|
|
|
geom3::eSpatialEmbedding embed_by_name(string ss) {
|
|
using namespace geom3;
|
|
auto& seo = spatial_embedding_options;
|
|
for(int i=0; i<isize(seo); i++) if(seo[i].first == ss) return eSpatialEmbedding(i);
|
|
bool numeric = true;
|
|
for(char c: ss) if(c < '0' || c > '9') numeric = false;
|
|
if(numeric) return eSpatialEmbedding(atoi(ss.c_str()));
|
|
for(int i=0; i<isize(seo); i++) if(appears(seo[i].first, ss)) return eSpatialEmbedding(i);
|
|
for(int i=0; i<isize(seo); i++) if(appears(seo[i].second, ss)) return eSpatialEmbedding(i);
|
|
return seNone;
|
|
}
|
|
|
|
#if CAP_COMMANDLINE
|
|
auto ah_embed = arg::add2("-seo", [] { arg::shift(); invoke_embed(embed_by_name(arg::args())); })
|
|
+ arg::add2("-never-invert", [] { never_invert = true; });
|
|
#endif
|
|
|
|
}
|