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hyperpoint adjusted for 3D geometry
This commit is contained in:
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Zeno Rogue
parent
c24fa20334
commit
dd0f573ca9
@ -845,7 +845,7 @@ void flip_z() {
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}
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hyperpoint coord_to_flat(ldcoord co) {
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hyperpoint res = hpxyz(0, 0, 0);
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hyperpoint res = Hypc;
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co = co - rug_center;
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for(int a=0; a<MAXDIM; a++)
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for(int b=0; b<3; b++)
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42
goldberg.cpp
42
goldberg.cpp
@ -454,31 +454,31 @@ namespace hr { namespace gp {
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}
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hyperpoint loctoh_ort(loc at) {
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return hpxyz(at.first, at.second, 1);
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return point3(at.first, at.second, 1);
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}
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hyperpoint corner_coords6[7] = {
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hpxyz(2, -1, 0),
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hpxyz(1, 1, 0),
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hpxyz(-1, 2, 0),
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hpxyz(-2, 1, 0),
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hpxyz(-1, -1, 0),
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hpxyz(1, -2, 0),
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hpxyz(0, 0, 0) // center, not a corner
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point3(2, -1, 0),
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point3(1, 1, 0),
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point3(-1, 2, 0),
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point3(-2, 1, 0),
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point3(-1, -1, 0),
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point3(1, -2, 0),
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point3(0, 0, 0) // center, not a corner
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};
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hyperpoint corner_coords4[7] = {
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hpxyz(1.5, -1.5, 0),
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// hpxyz(1, 0, 0),
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hpxyz(1.5, 1.5, 0),
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// hpxyz(0, 1, 0),
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hpxyz(-1.5, 1.5, 0),
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// hpxyz(-1, 0, 0),
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hpxyz(-1.5, -1.5, 0),
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// hpxyz(0, -1, 0),
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hpxyz(0, 0, 0),
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hpxyz(0, 0, 0),
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hpxyz(0, 0, 0)
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point3(1.5, -1.5, 0),
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// point3(1, 0, 0),
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point3(1.5, 1.5, 0),
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// point3(0, 1, 0),
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point3(-1.5, 1.5, 0),
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// point3(-1, 0, 0),
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point3(-1.5, -1.5, 0),
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// point3(0, -1, 0),
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point3(0, 0, 0),
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point3(0, 0, 0),
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point3(0, 0, 0)
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};
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#define corner_coords (S3==3 ? corner_coords6 : corner_coords4)
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@ -486,7 +486,7 @@ namespace hr { namespace gp {
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hyperpoint cornmul(const transmatrix& corners, const hyperpoint& c) {
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if(sphere && S3 == 3) {
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ld cmin = c[0] * c[1] * c[2] * (6 - S7);
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return corners * hpxyz(c[0] + cmin, c[1] + cmin, c[2] + cmin);
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return corners * point3(c[0] + cmin, c[1] + cmin, c[2] + cmin);
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}
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else return corners * c;
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}
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@ -564,7 +564,7 @@ namespace hr { namespace gp {
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area = ((2*x+y) * (2*x+y) + y*y*3) / 4;
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else
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area = x * x + y * y;
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next = hpxyz(x+y/2., -y * sqrt(3) / 2, 0);
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next = point3(x+y/2., -y * sqrt(3) / 2, 0);
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ld scale = 1 / hypot2(next);
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crossf *= scale;
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hepvdist *= scale;
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61
hyper.h
61
hyper.h
@ -189,22 +189,33 @@ typedef complex<ld> cld;
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#define DEBSM(x)
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struct hyperpoint : array<ld, 3> {
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#define DIM 2
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#define MDIM (DIM+1)
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#if DIM == 2
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#define D3(x) // x
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#define DC(x,y) // x,y
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#else
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#define D3(x) x
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#define DC(x,y) x,y
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#endif
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struct hyperpoint : array<ld, MDIM> {
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hyperpoint() {}
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hyperpoint(ld x, ld y, ld z) { (*this)[0] = x; (*this)[1] = y; (*this)[2] = z; }
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hyperpoint(ld x, ld y, ld z DC(, ld w)) { (*this)[0] = x; (*this)[1] = y; (*this)[2] = z; D3((*this)[3] = w;) }
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};
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struct transmatrix {
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ld tab[3][3];
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ld tab[MDIM][MDIM];
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ld * operator [] (int i) { return tab[i]; }
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const ld * operator [] (int i) const { return tab[i]; }
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};
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inline hyperpoint operator * (const transmatrix& T, const hyperpoint& H) {
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hyperpoint z;
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for(int i=0; i<3; i++) {
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for(int i=0; i<MDIM; i++) {
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z[i] = 0;
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for(int j=0; j<3; j++) z[i] += T[i][j] * H[j];
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for(int j=0; j<MDIM; j++) z[i] += T[i][j] * H[j];
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}
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return z;
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}
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@ -212,50 +223,65 @@ inline hyperpoint operator * (const transmatrix& T, const hyperpoint& H) {
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inline transmatrix operator * (const transmatrix& T, const transmatrix& U) {
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transmatrix R;
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// for(int i=0; i<3; i++) for(int j=0; j<3; j++) R[i][j] = 0;
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for(int i=0; i<3; i++) for(int j=0; j<3; j++) // for(int k=0; k<3; k++)
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for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++) // for(int k=0; k<3; k++)
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R[i][j] = T[i][0] * U[0][j] + T[i][1] * U[1][j] + T[i][2] * U[2][j];
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return R;
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}
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constexpr transmatrix diag(ld a, ld b, ld c, ld d) {
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#if DIM==2
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return transmatrix{{{a,0,0}, {0,b,0}, {0,0,c}}};
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#else
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return transmatrix{{{a,0,0,0}, {0,b,0,0}, {0,0,c,0}, {0,0,0,d}}};
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#endif
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}
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// identity matrix
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const static transmatrix Id = {{{1,0,0}, {0,1,0}, {0,0,1}}};
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const static transmatrix Id = diag(1,1,1,1);
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// mirror image
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const static transmatrix Mirror = {{{1,0,0}, {0,-1,0}, {0,0,1}}};
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const static transmatrix Mirror = diag(1,-1,1,1);
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// mirror image
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const static transmatrix MirrorX = {{{-1,0,0}, {0,1,0}, {0,0,1}}};
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const static transmatrix MirrorX = diag(-1,1,1,1);
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// mirror image
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const static transmatrix MirrorZ = {{{1,0,0}, {0,1,0}, {0,0,-1}}};
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const static transmatrix MirrorZ = diag(1,1,-1,1);
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// rotate by PI
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const static transmatrix pispin = {{{-1,0,0}, {0,-1,0}, {0,0,1}}};
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const static transmatrix pispin = diag(-1,-1,1,1);
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// central symmetry
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const static transmatrix centralsym = {{{-1,0,0}, {0,-1,0}, {0,0,-1}}};
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const static transmatrix centralsym = diag(-1,-1,-1,-1);
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#define hpxyz hyperpoint
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#if DIM == 3
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hyperpoint point3(ld x, ld y, ld z) { return hpxyz(x,y,z,0); }
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#else
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#define point3 hpxyz
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#endif
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namespace hyperpoint_vec {
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inline hyperpoint& operator *= (hyperpoint& h, ld d) {
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h[0] *= d; h[1] *= d; h[2] *= d;
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for(int i=0; i<MDIM; i++) h[i] *= d;
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return h;
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}
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inline hyperpoint& operator /= (hyperpoint& h, ld d) {
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h[0] /= d; h[1] /= d; h[2] /= d;
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for(int i=0; i<MDIM; i++) h[i] /= d;
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return h;
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}
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inline hyperpoint operator += (hyperpoint& h, hyperpoint h2) {
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for(int i: {0,1,2}) h[i] += h2[i];
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for(int i=0; i<MDIM; i++) h[i] += h2[i];
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return h;
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}
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inline hyperpoint operator -= (hyperpoint& h, hyperpoint h2) {
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for(int i: {0,1,2}) h[i] -= h2[i];
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for(int i=0; i<MDIM; i++) h[i] -= h2[i];
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return h;
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}
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@ -271,12 +297,13 @@ namespace hyperpoint_vec {
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h1[1] * h2[2] - h1[2] * h2[1],
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h1[2] * h2[0] - h1[0] * h2[2],
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h1[0] * h2[1] - h1[1] * h2[0]
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DC(,0)
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);
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}
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// inner product (in R^3)
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inline ld operator | (hyperpoint h1, hyperpoint h2) {
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return h1[0] * h2[0] + h1[1] * h2[1] + h1[2] * h2[2];
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return h1[0] * h2[0] + h1[1] * h2[1] + h1[2] * h2[2] D3(+ h1[3] * h2[3]);
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}
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}
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340
hyperpoint.cpp
340
hyperpoint.cpp
@ -37,7 +37,7 @@ ld inverse_tanh(ld x) { return log((1+x)/(1-x)) / 2; } */
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ld squar(ld x) { return x*x; }
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int sig(int z) { return (sphere || z<2)?1:-1; }
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int sig(int z) { return (sphere || z<DIM)?1:-1; }
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int curvature() {
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switch(cgclass) {
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@ -118,65 +118,67 @@ ld atan2_auto(ld y, ld x) {
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// by points in 3D space (Minkowski space) such that x^2+y^2-z^2 == -1, z > 0
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// (this is analogous to representing a sphere with points such that x^2+y^2+z^2 == 1)
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hyperpoint hpxy(ld x, ld y) {
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return hpxyz(x,y, euclid ? 1 : sphere ? sqrt(1-x*x-y*y) : sqrt(1+x*x+y*y));
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hyperpoint hpxy(ld x, ld y DC(, ld z)) {
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return hpxyz(x,y,DC(z,) euclid ? 1 : sphere ? sqrt(1-x*x-y*y D3(-z*z)) : sqrt(1+x*x+y*y D3(+z*z)));
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}
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// center of the pseudosphere
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const hyperpoint Hypc(0,0,0);
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const hyperpoint Hypc(0,0,0 DC(,0));
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// origin of the hyperbolic plane
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const hyperpoint C0(0,0,1);
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const hyperpoint C0(0,0 DC(,0) ,1);
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// a point (I hope this number needs no comments ;) )
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const hyperpoint Cx1(1,0,1.41421356237);
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const hyperpoint Cx1(1,0 DC(,0) ,1.41421356237);
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// this function returns approximate square of distance between two points
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// (in the spherical analogy, this would be the distance in the 3D space,
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// through the interior, not on the surface)
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// also used to verify whether a point h1 is on the hyperbolic plane by using Hypc for h2
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bool zero2(hyperpoint h) { return h[0] == 0 && h[1] == 0; }
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bool zero2(hyperpoint h) { return h[0] == 0 && h[1] == 0 D3(&& h[2] == 0); }
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bool zero3(hyperpoint h) { return h[0] == 0 && h[1] == 0 && h[2] == 0; }
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bool zero3(hyperpoint h) { return h[0] == 0 && h[1] == 0 && h[2] == 0 D3(&& h[3] == 0); }
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ld intval(const hyperpoint &h1, const hyperpoint &h2) {
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ld res = 0;
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for(int i=0; i<MDIM; i++) res += squar(h1[i] - h2[i]) * sig(i);
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if(elliptic) {
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double d1 = squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + squar(h1[2]-h2[2]);
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double d2 = squar(h1[0]+h2[0]) + squar(h1[1]+h2[1]) + squar(h1[2]+h2[2]);
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return min(d1, d2);
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ld res2 = 0;
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for(int i=0; i<MDIM; i++) res2 += squar(h1[i] + h2[i]) * sig(i);
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return min(res, res2);
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}
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + (sphere?1:euclid?0:-1) * squar(h1[2]-h2[2]);
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return res;
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}
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ld intvalxy(const hyperpoint &h1, const hyperpoint &h2) {
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]);
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) D3(+ squar(h1[2]-h2[2]));
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}
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ld intvalxyz(const hyperpoint &h1, const hyperpoint &h2) {
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + squar(h1[2]-h2[2]);
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return squar(h1[0]-h2[0]) + squar(h1[1]-h2[1]) + squar(h1[2]-h2[2]) D3(+ squar(h1[3]-h2[3]));
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}
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ld hypot2(const hyperpoint& h) {
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return sqrt(h[0]*h[0]+h[1]*h[1]);
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}
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ld hypot3(const hyperpoint& h) {
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return sqrt(h[0]*h[0]+h[1]*h[1]+h[2]*h[2]);
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}
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ld sqhypot2(const hyperpoint& h) {
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return h[0]*h[0]+h[1]*h[1];
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return h[0]*h[0]+h[1]*h[1] D3(+h[2]*h[2]);
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}
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ld sqhypot3(const hyperpoint& h) {
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return h[0]*h[0]+h[1]*h[1]+h[2]*h[2];
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return h[0]*h[0]+h[1]*h[1]+h[2]*h[2] D3(+h[3]*h[3]);
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}
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ld hypot2(const hyperpoint& h) {
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return sqrt(sqhypot2(h));
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}
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ld hypot3(const hyperpoint& h) {
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return sqrt(sqhypot3(h));
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}
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ld zlevel(const hyperpoint &h) {
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if(euclid) return h[2];
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if(euclid) return h[DIM];
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else if(sphere) return sqrt(intval(h, Hypc));
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else return (h[2] < 0 ? -1 : 1) * sqrt(-intval(h, Hypc));
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else return (h[DIM] < 0 ? -1 : 1) * sqrt(-intval(h, Hypc));
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}
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ld hypot_auto(ld x, ld y) {
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@ -195,7 +197,7 @@ ld hypot_auto(ld x, ld y) {
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// move H back to the sphere/hyperboloid/plane
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hyperpoint normalize(hyperpoint H) {
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ld Z = zlevel(H);
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for(int c=0; c<3; c++) H[c] /= Z;
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for(int c=0; c<MDIM; c++) H[c] /= Z;
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return H;
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}
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@ -213,7 +215,7 @@ hyperpoint midz(const hyperpoint& H1, const hyperpoint& H2) {
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ld Z = 2;
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if(!euclid) Z = zlevel(H3) * 2 / (zlevel(H1) + zlevel(H2));
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for(int c=0; c<3; c++) H3[c] /= Z;
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for(int c=0; c<MDIM; c++) H3[c] /= Z;
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return H3;
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}
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@ -225,25 +227,26 @@ hyperpoint midz(const hyperpoint& H1, const hyperpoint& H2) {
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// (just like isometries of the sphere are represented by rotation matrices)
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// rotate by alpha degrees
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transmatrix spin(ld alpha) {
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transmatrix cspin(int a, int b, ld alpha) {
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transmatrix T = Id;
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T[0][0] = +cos(alpha); T[0][1] = +sin(alpha);
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T[1][0] = -sin(alpha); T[1][1] = +cos(alpha);
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T[2][2] = 1;
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T[a][a] = +cos(alpha); T[a][b] = +sin(alpha);
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T[b][a] = -sin(alpha); T[b][b] = +cos(alpha);
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return T;
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}
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transmatrix eupush(ld x, ld y) {
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transmatrix spin(ld alpha) { return cspin(0, 1, alpha); }
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transmatrix eupush(ld x, ld y DC(, ld z)) {
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transmatrix T = Id;
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T[0][2] = x;
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T[1][2] = y;
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T[0][DIM] = x;
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T[1][DIM] = y;
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D3( T[2][DIM] = z );
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return T;
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}
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transmatrix eupush(hyperpoint h) {
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transmatrix T = Id;
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T[0][2] = h[0];
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T[1][2] = h[1];
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for(int i=0; i<DIM; i++) T[i][DIM] = h[i];
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return T;
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}
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@ -263,183 +266,202 @@ transmatrix euaffine(hyperpoint h) {
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return T;
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}
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// push alpha units to the right
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transmatrix xpush(ld alpha) {
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if(euclid) return eupush(alpha, 0);
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transmatrix cpush(int cid, ld alpha) {
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transmatrix T = Id;
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if(sphere) {
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T[0][0] = +cos(alpha); T[0][2] = +sin(alpha);
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T[2][0] = -sin(alpha); T[2][2] = +cos(alpha);
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}
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else {
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T[0][0] = +cosh(alpha); T[0][2] = +sinh(alpha);
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T[2][0] = +sinh(alpha); T[2][2] = +cosh(alpha);
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}
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T[DIM][DIM] = T[cid][cid] = cos_auto(alpha);
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T[cid][DIM] = sin_auto(alpha);
|
||||
T[DIM][cid] = -curvature() * sin_auto(alpha);
|
||||
return T;
|
||||
}
|
||||
|
||||
inline hyperpoint xpush0(ld x) {
|
||||
hyperpoint h;
|
||||
if(euclid) return hpxy(x, 0);
|
||||
else if(sphere) h[0] = sin(x), h[1] = 0, h[2] = cos(x);
|
||||
else h[0] = sinh(x), h[1] = 0, h[2] = cosh(x);
|
||||
// push alpha units to the right
|
||||
transmatrix xpush(ld alpha) { return cpush(0, alpha); }
|
||||
|
||||
inline hyperpoint cpush0(int c, ld x) {
|
||||
hyperpoint h = Hypc;
|
||||
h[DIM] = cos_auto(x);
|
||||
h[c] = sin_auto(x);
|
||||
return h;
|
||||
}
|
||||
|
||||
inline hyperpoint ypush0(ld x) {
|
||||
hyperpoint h;
|
||||
if(euclid) return hpxy(x, 0);
|
||||
else if(sphere) h[0] = 0, h[1] = sin(x), h[2] = cos(x);
|
||||
else h[0] = 0, h[1] = sinh(x), h[2] = cosh(x);
|
||||
return h;
|
||||
}
|
||||
inline hyperpoint xpush0(ld x) { return cpush0(0, x); }
|
||||
|
||||
inline hyperpoint ypush0(ld x) { return cpush0(1, x); }
|
||||
|
||||
inline hyperpoint xspinpush0(ld alpha, ld x) {
|
||||
// return spin(alpha)*xpush0(x);
|
||||
ld s;
|
||||
hyperpoint h;
|
||||
if(euclid) return hpxy(x*cos(alpha), -x*sin(alpha));
|
||||
else if(sphere) s=sin(x), h[0] = s*cos(alpha), h[1] = -s*sin(alpha), h[2] = cos(x);
|
||||
else s=sinh(x), h[0] = s*cos(alpha), h[1] = -s*sin(alpha), h[2] = cosh(x);
|
||||
hyperpoint h = Hypc;
|
||||
h[DIM] = cos_auto(x);
|
||||
h[0] = sin_auto(x) * cos(alpha);
|
||||
h[1] = sin_auto(x) * -sin(alpha);
|
||||
return h;
|
||||
}
|
||||
|
||||
// push alpha units vertically
|
||||
transmatrix ypush(ld alpha) {
|
||||
if(euclid) return eupush(0, alpha);
|
||||
transmatrix T = Id;
|
||||
if(sphere) {
|
||||
T[1][1] = +cos(alpha); T[1][2] = +sin(alpha);
|
||||
T[2][1] = -sin(alpha); T[2][2] = +cos(alpha);
|
||||
}
|
||||
transmatrix ypush(ld alpha) { return cpush(1, alpha); }
|
||||
|
||||
transmatrix parabolic1(ld u DC(, ld v)) {
|
||||
if(euclid)
|
||||
return ypush(u);
|
||||
else {
|
||||
T[1][1] = +cosh(alpha); T[1][2] = +sinh(alpha);
|
||||
T[2][1] = +sinh(alpha); T[2][2] = +cosh(alpha);
|
||||
ld diag = (u*u D3(+v*v))/2;
|
||||
#if DIM==2
|
||||
return transmatrix {{{-diag+1, u, diag}, {-u, 1, u}, {-diag, u, diag+1}}};
|
||||
#else
|
||||
return transmatrix {{{-diag+1, u, v, diag}, {-u, 1, 0, u}, {-v, 0, 1, v}, {-diag, u, v, diag+1}}};
|
||||
#endif
|
||||
}
|
||||
}
|
||||
|
||||
transmatrix spintoc(const hyperpoint& H, int t, int f) {
|
||||
transmatrix T = Id;
|
||||
ld R = hypot(H[f], H[t]);
|
||||
if(R >= 1e-12) {
|
||||
T[t][t] = +H[t]/R; T[t][f] = +H[f]/R;
|
||||
T[f][t] = -H[f]/R; T[f][f] = +H[t]/R;
|
||||
}
|
||||
return T;
|
||||
}
|
||||
|
||||
transmatrix parabolic1(ld u) {
|
||||
if(euclid)
|
||||
return ypush(u);
|
||||
else
|
||||
return transmatrix {{{-u*u/2+1, u, u*u/2}, {-u, 1, u}, {-u*u/2, u, u*u/2+1}}};
|
||||
transmatrix rspintoc(const hyperpoint& H, int t, int f) {
|
||||
transmatrix T = Id;
|
||||
ld R = hypot(H[f], H[t]);
|
||||
if(R >= 1e-12) {
|
||||
T[t][t] = +H[t]/R; T[t][f] = -H[f]/R;
|
||||
T[f][t] = +H[f]/R; T[f][f] = +H[t]/R;
|
||||
}
|
||||
return T;
|
||||
}
|
||||
|
||||
// rotate the hyperbolic plane around C0 such that H[1] == 0 and H[0] >= 0
|
||||
transmatrix spintox(const hyperpoint& H) {
|
||||
transmatrix T = Id;
|
||||
ld R = sqrt(H[0] * H[0] + H[1] * H[1]);
|
||||
if(R >= 1e-12) {
|
||||
T[0][0] = +H[0]/R; T[0][1] = +H[1]/R;
|
||||
T[1][0] = -H[1]/R; T[1][1] = +H[0]/R;
|
||||
}
|
||||
return T;
|
||||
transmatrix spintox(const hyperpoint& H) {
|
||||
#if DIM==2
|
||||
return spintoc(H, 0, 1);
|
||||
#else
|
||||
transmatrix T1 = spintoc(H, 0, 1);
|
||||
return spintoc(T1*H, 0, 2) * T1;
|
||||
#endif
|
||||
}
|
||||
|
||||
void set_column(transmatrix& T, int i, const hyperpoint& H) {
|
||||
for(int j=0; j<3; j++)
|
||||
for(int j=0; j<MDIM; j++)
|
||||
T[j][i] = H[j];
|
||||
}
|
||||
|
||||
transmatrix build_matrix(hyperpoint h1, hyperpoint h2, hyperpoint h3) {
|
||||
transmatrix T;
|
||||
for(int i=0; i<3; i++)
|
||||
for(int i=0; i<MDIM; i++)
|
||||
T[i][0] = h1[i],
|
||||
T[i][1] = h2[i],
|
||||
T[i][2] = h3[i];
|
||||
T[i][2] = h3[i]
|
||||
DC(, T[i][3] = 0);
|
||||
return T;
|
||||
}
|
||||
|
||||
// reverse of spintox(H)
|
||||
transmatrix rspintox(const hyperpoint& H) {
|
||||
transmatrix T = Id;
|
||||
ld R = sqrt(H[0] * H[0] + H[1] * H[1]);
|
||||
if(R >= 1e-12) {
|
||||
T[0][0] = +H[0]/R; T[0][1] = -H[1]/R;
|
||||
T[1][0] = +H[1]/R; T[1][1] = +H[0]/R;
|
||||
}
|
||||
return T;
|
||||
transmatrix rspintox(const hyperpoint& H) {
|
||||
#if DIM==2
|
||||
return rspintoc(H, 0, 1);
|
||||
#else
|
||||
transmatrix T1 = spintoc(H, 0, 1);
|
||||
return rspintoc(H, 0, 1) * rspintoc(T1*H, 0, 2);
|
||||
#endif
|
||||
}
|
||||
|
||||
// for H such that H[1] == 0, this matrix pushes H to C0
|
||||
transmatrix pushxto0(const hyperpoint& H) {
|
||||
if(euclid) return eupush(-H[0], -H[1]);
|
||||
transmatrix T = Id;
|
||||
if(sphere) {
|
||||
T[0][0] = +H[2]; T[0][2] = -H[0];
|
||||
T[2][0] = +H[0]; T[2][2] = +H[2];
|
||||
}
|
||||
else {
|
||||
T[0][0] = +H[2]; T[0][2] = -H[0];
|
||||
T[2][0] = -H[0]; T[2][2] = +H[2];
|
||||
}
|
||||
T[0][0] = +H[DIM]; T[0][DIM] = -H[0];
|
||||
T[DIM][0] = curvature() * H[0]; T[DIM][DIM] = +H[DIM];
|
||||
return T;
|
||||
}
|
||||
|
||||
// reverse of pushxto0(H)
|
||||
transmatrix rpushxto0(const hyperpoint& H) {
|
||||
if(euclid) return eupush(H[0], H[1]);
|
||||
transmatrix T = Id;
|
||||
if(sphere) {
|
||||
T[0][0] = +H[2]; T[0][2] = +H[0];
|
||||
T[2][0] = -H[0]; T[2][2] = +H[2];
|
||||
}
|
||||
else {
|
||||
T[0][0] = +H[2]; T[0][2] = +H[0];
|
||||
T[2][0] = +H[0]; T[2][2] = +H[2];
|
||||
}
|
||||
T[0][0] = +H[DIM]; T[0][DIM] = H[0];
|
||||
T[DIM][0] = -curvature() * H[0]; T[DIM][DIM] = +H[DIM];
|
||||
return T;
|
||||
}
|
||||
|
||||
transmatrix ggpushxto0(const hyperpoint& H, ld co) {
|
||||
if(euclid) return eupush(co * H[0], co * H[1] DC(, co * H[2]));
|
||||
transmatrix res = Id;
|
||||
if(sqhypot2(H) < 1e-12) return res;
|
||||
ld fac = (H[DIM]-1) / sqhypot2(H);
|
||||
for(int i=0; i<DIM; i++)
|
||||
for(int j=0; j<DIM; j++)
|
||||
res[i][j] += H[i] * H[j] * fac;
|
||||
|
||||
for(int d=0; d<DIM; d++)
|
||||
res[d][DIM] = co * H[d],
|
||||
res[DIM][d] = -curvature() * co * H[d];
|
||||
res[DIM][DIM] = H[DIM];
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
// generalization: H[1] can be non-zero
|
||||
transmatrix gpushxto0(const hyperpoint& H) {
|
||||
if(euclid) return eupush(-H[0], -H[1]);
|
||||
hyperpoint H2 = spintox(H) * H;
|
||||
return rspintox(H) * pushxto0(H2) * spintox(H);
|
||||
return ggpushxto0(H, -1);
|
||||
}
|
||||
|
||||
transmatrix rgpushxto0(const hyperpoint& H) {
|
||||
if(euclid) return eupush(H[0], H[1]);
|
||||
hyperpoint H2 = spintox(H) * H;
|
||||
return rspintox(H) * rpushxto0(H2) * spintox(H);
|
||||
return ggpushxto0(H, 1);
|
||||
}
|
||||
|
||||
|
||||
// fix the matrix T so that it is indeed an isometry
|
||||
// (without using this, imprecision could accumulate)
|
||||
|
||||
void fixmatrix(transmatrix& T) {
|
||||
if(euclid) {
|
||||
for(int x=0; x<2; x++) for(int y=0; y<=x; y++) {
|
||||
for(int x=0; x<DIM; x++) for(int y=0; y<=x; y++) {
|
||||
ld dp = 0;
|
||||
for(int z=0; z<2; z++) dp += T[z][x] * T[z][y];
|
||||
for(int z=0; z<DIM; z++) dp += T[z][x] * T[z][y];
|
||||
|
||||
if(y == x) dp = 1 - sqrt(1/dp);
|
||||
|
||||
for(int z=0; z<2; z++) T[z][x] -= dp * T[z][y];
|
||||
for(int z=0; z<DIM; z++) T[z][x] -= dp * T[z][y];
|
||||
}
|
||||
for(int x=0; x<2; x++) T[2][x] = 0;
|
||||
for(int x=0; x<DIM; x++) T[2][x] = 0;
|
||||
T[2][2] = 1;
|
||||
}
|
||||
else for(int x=0; x<3; x++) for(int y=0; y<=x; y++) {
|
||||
else for(int x=0; x<MDIM; x++) for(int y=0; y<=x; y++) {
|
||||
ld dp = 0;
|
||||
for(int z=0; z<3; z++) dp += T[z][x] * T[z][y] * sig(z);
|
||||
for(int z=0; z<MDIM; z++) dp += T[z][x] * T[z][y] * sig(z);
|
||||
|
||||
if(y == x) dp = 1 - sqrt(sig(x)/dp);
|
||||
|
||||
for(int z=0; z<3; z++) T[z][x] -= dp * T[z][y];
|
||||
for(int z=0; z<MDIM; z++) T[z][x] -= dp * T[z][y];
|
||||
}
|
||||
}
|
||||
|
||||
// show the matrix on screen
|
||||
|
||||
ld det(const transmatrix& T) {
|
||||
#if DIM == 3
|
||||
ld det = 0;
|
||||
for(int i=0; i<3; i++)
|
||||
det += T[0][i] * T[1][(i+1)%3] * T[2][(i+2)%3];
|
||||
for(int i=0; i<3; i++)
|
||||
det -= T[0][i] * T[1][(i+2)%3] * T[2][(i+1)%3];
|
||||
#else
|
||||
ld det = 1;
|
||||
transmatrix M = T;
|
||||
for(int a=0; a<MDIM; a++) {
|
||||
for(int b=a; b<=DIM; b++)
|
||||
if(M[b][a]) {
|
||||
if(b != a)
|
||||
for(int c=a; c<MDIM; c++) tie(M[b][c], M[a][c]) = make_pair(-M[a][c], M[b][c]);
|
||||
break;
|
||||
}
|
||||
if(!M[a][a]) return 0;
|
||||
for(int b=a+1; b<=DIM; b++) {
|
||||
ld co = -M[b][a] / M[a][a];
|
||||
for(int c=a; c<MDIM; c++) M[b][c] += M[a][c] * co;
|
||||
}
|
||||
det *= M[a][a];
|
||||
}
|
||||
#endif
|
||||
return det;
|
||||
}
|
||||
|
||||
@ -450,6 +472,7 @@ void inverse_error(const transmatrix& T) {
|
||||
transmatrix inverse(const transmatrix& T) {
|
||||
profile_start(7);
|
||||
|
||||
#if DIM == 3
|
||||
ld d = det(T);
|
||||
transmatrix T2;
|
||||
if(d == 0) {
|
||||
@ -460,6 +483,36 @@ transmatrix inverse(const transmatrix& T) {
|
||||
for(int i=0; i<3; i++)
|
||||
for(int j=0; j<3; j++)
|
||||
T2[j][i] = (T[(i+1)%3][(j+1)%3] * T[(i+2)%3][(j+2)%3] - T[(i+1)%3][(j+2)%3] * T[(i+2)%3][(j+1)%3]) / d;
|
||||
|
||||
#else
|
||||
transmatrix T1 = T;
|
||||
transmatrix T2 = Id;
|
||||
|
||||
for(int a=0; a<MDIM; a++) {
|
||||
for(int b=a; b<=DIM; b++)
|
||||
if(T1[b][a]) {
|
||||
if(b != a)
|
||||
for(int c=0; c<MDIM; c++)
|
||||
tie(T1[b][c], T1[a][c]) = make_pair(T1[a][c], T1[b][c]),
|
||||
tie(T2[b][c], T2[a][c]) = make_pair(T2[a][c], T2[b][c]);
|
||||
break;
|
||||
}
|
||||
if(!T1[a][a]) { inverse_error(T); return Id; }
|
||||
for(int b=a+1; b<=DIM; b++) {
|
||||
ld co = -T1[b][a] / T1[a][a];
|
||||
for(int c=0; c<MDIM; c++) T1[b][c] += T1[a][c] * co, T2[b][c] += T2[a][c] * co;
|
||||
}
|
||||
}
|
||||
|
||||
for(int a=MDIM-1; a>=0; a--) {
|
||||
for(int b=0; b<a; b++) {
|
||||
ld co = -T1[b][a] / T1[a][a];
|
||||
for(int c=0; c<MDIM; c++) T1[b][c] += T1[a][c] * co, T2[b][c] += T2[a][c] * co;
|
||||
}
|
||||
ld co = 1 / T1[a][a];
|
||||
for(int c=0; c<MDIM; c++) T1[a][c] *= co, T2[a][c] *= co;
|
||||
}
|
||||
#endif
|
||||
|
||||
profile_stop(7);
|
||||
return T2;
|
||||
@ -469,14 +522,14 @@ transmatrix inverse(const transmatrix& T) {
|
||||
double hdist0(const hyperpoint& mh) {
|
||||
switch(cgclass) {
|
||||
case gcHyperbolic:
|
||||
if(mh[2] < 1) return 0;
|
||||
return acosh(mh[2]);
|
||||
if(mh[DIM] < 1) return 0;
|
||||
return acosh(mh[DIM]);
|
||||
case gcEuclid: {
|
||||
ld d = sqrt(mh[0]*mh[0]+mh[1]*mh[1]);
|
||||
ld d = sqhypot2(mh);
|
||||
return d;
|
||||
}
|
||||
case gcSphere: {
|
||||
ld res = mh[2] >= 1 ? 0 : mh[2] <= -1 ? M_PI : acos(mh[2]);
|
||||
ld res = mh[DIM] >= 1 ? 0 : mh[DIM] <= -1 ? M_PI : acos(mh[DIM]);
|
||||
if(elliptic && res > M_PI/2) res = M_PI-res;
|
||||
return res;
|
||||
}
|
||||
@ -516,31 +569,31 @@ double hdist(const hyperpoint& h1, const hyperpoint& h2) {
|
||||
|
||||
hyperpoint mscale(const hyperpoint& t, double fac) {
|
||||
hyperpoint res;
|
||||
for(int i=0; i<3; i++)
|
||||
for(int i=0; i<MDIM; i++)
|
||||
res[i] = t[i] * fac;
|
||||
return res;
|
||||
}
|
||||
|
||||
transmatrix mscale(const transmatrix& t, double fac) {
|
||||
transmatrix res;
|
||||
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
|
||||
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
|
||||
res[i][j] = t[i][j] * fac;
|
||||
return res;
|
||||
}
|
||||
|
||||
transmatrix xyscale(const transmatrix& t, double fac) {
|
||||
transmatrix res;
|
||||
for(int i=0; i<3; i++) for(int j=0; j<2; j++)
|
||||
for(int i=0; i<MDIM; i++) for(int j=0; j<DIM; j++)
|
||||
res[i][j] = t[i][j] * fac;
|
||||
return res;
|
||||
}
|
||||
|
||||
transmatrix xyzscale(const transmatrix& t, double fac, double facz) {
|
||||
transmatrix res;
|
||||
for(int i=0; i<3; i++) for(int j=0; j<2; j++)
|
||||
for(int i=0; i<MDIM; i++) for(int j=0; j<DIM; j++)
|
||||
res[i][j] = t[i][j] * fac;
|
||||
for(int i=0; i<3; i++)
|
||||
res[i][2] = t[i][2] * facz;
|
||||
for(int i=0; i<MDIM; i++)
|
||||
res[i][DIM] = t[i][DIM] * facz;
|
||||
return res;
|
||||
}
|
||||
|
||||
@ -554,7 +607,7 @@ transmatrix mzscale(const transmatrix& t, double fac) {
|
||||
transmatrix res = t * inverse(tcentered) * ypush(-fac) * tcentered;
|
||||
fac *= .2;
|
||||
fac += 1;
|
||||
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
|
||||
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
|
||||
res[i][j] = res[i][j] * fac;
|
||||
return res;
|
||||
}
|
||||
@ -562,7 +615,8 @@ transmatrix mzscale(const transmatrix& t, double fac) {
|
||||
transmatrix pushone() { return euclid ? eupush(1, 0) : xpush(sphere?.5 : 1); }
|
||||
|
||||
bool operator == (hyperpoint h1, hyperpoint h2) {
|
||||
return h1[0] == h2[0] && h1[1] == h2[1] && h1[2] == h2[2];
|
||||
for(int i=0; i<MDIM; i++) if(h1[i] != h2[i]) return false;
|
||||
return true;
|
||||
}
|
||||
|
||||
// rotation matrix in R^3
|
||||
|
||||
12
hypgraph.cpp
12
hypgraph.cpp
@ -85,7 +85,7 @@ hyperpoint gethyper(ld x, ld y) {
|
||||
|
||||
if(vid.camera_angle) camrotate(hx, hy);
|
||||
|
||||
return perspective_to_space(hpxyz(hx, hy, 0));
|
||||
return perspective_to_space(hpxyz(hx, hy, 0 DC(,0)));
|
||||
}
|
||||
|
||||
void ballmodel(hyperpoint& ret, double alpha, double d, double zl) {
|
||||
@ -171,8 +171,8 @@ template<class T> void makeband(hyperpoint H, hyperpoint& ret, const T& f) {
|
||||
y = asin_auto(H[1]);
|
||||
x = asin_auto_clamp(H[0] / cos_auto(y)) + band_shift;
|
||||
if(sphere) {
|
||||
if(H[2] < 0 && x > 0) x = M_PI - x;
|
||||
else if(H[2] < 0 && x <= 0) x = -M_PI - x;
|
||||
if(H[DIM] < 0 && x > 0) x = M_PI - x;
|
||||
else if(H[DIM] < 0 && x <= 0) x = -M_PI - x;
|
||||
}
|
||||
hypot_zlev(zlev, y, yf, zf);
|
||||
|
||||
@ -180,7 +180,7 @@ template<class T> void makeband(hyperpoint H, hyperpoint& ret, const T& f) {
|
||||
|
||||
ld yzf = y * zf; y *= yf;
|
||||
conformal::apply_orientation(y, x);
|
||||
ret = hpxyz(x / M_PI, y / M_PI, 0);
|
||||
ret = hpxyz(x / M_PI, y / M_PI, 0 DC(,0));
|
||||
if(zlev != 1 && current_display->stereo_active())
|
||||
apply_depth(ret, yzf / M_PI);
|
||||
return;
|
||||
@ -319,7 +319,7 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
|
||||
case gcEuclid: {
|
||||
// stereographic projection to a sphere
|
||||
auto hd = hdist0(H) / vid.euclid_to_sphere;
|
||||
if(hd == 0) ret = hpxyz(0, 0, -1);
|
||||
if(hd == 0) ret = hpxyz(0, 0, -1 DC(,0));
|
||||
else {
|
||||
ld x = 2 * hd / (1 + hd * hd);
|
||||
ld y = x / hd;
|
||||
@ -391,7 +391,7 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
|
||||
cld w(ret[0], ret[1]);
|
||||
cld z = sqrt(c4*w*w-c1) + c2*w;
|
||||
if(abs(z) > 1) z = c1 / z;
|
||||
hyperpoint zr = hpxyz(real(z), imag(z), 0);
|
||||
hyperpoint zr = hpxyz(real(z), imag(z), 0 DC(,0));
|
||||
|
||||
hyperpoint inhyp = perspective_to_space(zr, 1, gcHyperbolic);
|
||||
last_skiprope = vid.skiprope;
|
||||
|
||||
@ -204,7 +204,7 @@ int rearrange(bool total, ld minedge) {
|
||||
for(int i=0; i<isize(cells); i++) {
|
||||
auto& p1 = cells[i];
|
||||
using namespace hyperpoint_vec;
|
||||
hyperpoint h = hpxyz(0, 0, 0);
|
||||
hyperpoint h = Hypc;
|
||||
for(auto v: p1.vertices) h = h + v;
|
||||
|
||||
bool changed = total;
|
||||
|
||||
@ -444,7 +444,7 @@ void drawTexturedTriangle(SDL_Surface *s, int *px, int *py, glvertex *tv, color_
|
||||
miny = min(miny, py[i]), maxy = max(maxy, py[i]);
|
||||
for(int mx=minx; mx<maxx; mx++)
|
||||
for(int my=miny; my<maxy; my++) {
|
||||
hyperpoint h = isource * hpxyz(mx, my, 1);
|
||||
hyperpoint h = isource * point3(mx, my, 1);
|
||||
if(h[0] >= -1e-7 && h[1] >= -1e-7 && h[2] >= -1e-7) {
|
||||
hyperpoint ht = target * h;
|
||||
int tw = texture::config.data.twidth;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user