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3D graphics in 2D (first commit)

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Zeno Rogue
2019-05-08 18:33:08 +02:00
parent ea768b634b
commit 1c4d86e0e9
27 changed files with 424 additions and 269 deletions
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100
hyperpoint.cpp
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@@ -38,7 +38,7 @@ ld inverse_tanh(ld x) { return log((1+x)/(1-x)) / 2; } */
ld squar(ld x) { return x*x; }
int sig(int z) { return (sphere || z<DIM)?1:-1; }
int sig(int z) { return (sphere || z<GDIM)?1:-1; }
int curvature() {
switch(cgclass) {
@@ -157,7 +157,7 @@ const hyperpoint C03 = hyperpoint(0,0,0,1);
const hyperpoint Cx12 = hyperpoint(1,0,1.41421356237,0);
const hyperpoint Cx13 = hyperpoint(1,0,0,1.41421356237);
#define Cx1 (DIM==2?Cx12:Cx13)
#define Cx1 (GDIM==2?Cx12:Cx13)
// this function returns approximate square of distance between two points
// (in the spherical analogy, this would be the distance in the 3D space,
@@ -191,9 +191,9 @@ ld hypot_d(int d, const hyperpoint& h) {
}
ld zlevel(const hyperpoint &h) {
if(euclid) return h[DIM];
if(euclid) return h[GDIM];
else if(sphere) return sqrt(intval(h, Hypc));
else return (h[DIM] < 0 ? -1 : 1) * sqrt(-intval(h, Hypc));
else return (h[GDIM] < 0 ? -1 : 1) * sqrt(-intval(h, Hypc));
}
ld hypot_auto(ld x, ld y) {
@@ -252,7 +252,7 @@ transmatrix cspin(int a, int b, ld alpha) {
transmatrix spin(ld alpha) { return cspin(0, 1, alpha); }
transmatrix random_spin() {
if(DIM == 2) return spin(randd() * 2 * M_PI);
if(GDIM == 2) return spin(randd() * 2 * M_PI);
else {
ld alpha2 = acos(randd() * 2 - 1);
ld alpha = randd() * 2 * M_PI;
@@ -263,22 +263,22 @@ transmatrix random_spin() {
transmatrix eupush(ld x, ld y) {
transmatrix T = Id;
T[0][DIM] = x;
T[1][DIM] = y;
T[0][GDIM] = x;
T[1][GDIM] = y;
return T;
}
transmatrix eupush3(ld x, ld y, ld z) {
transmatrix T = Id;
T[0][DIM] = x;
T[1][DIM] = y;
if(DIM == 3) T[2][DIM] = z;
T[0][GDIM] = x;
T[1][GDIM] = y;
if(GDIM == 3) T[2][GDIM] = z;
return T;
}
transmatrix eupush(hyperpoint h) {
transmatrix T = Id;
for(int i=0; i<DIM; i++) T[i][DIM] = h[i];
for(int i=0; i<GDIM; i++) T[i][GDIM] = h[i];
return T;
}
@@ -300,9 +300,9 @@ transmatrix euaffine(hyperpoint h) {
transmatrix cpush(int cid, ld alpha) {
transmatrix T = Id;
T[DIM][DIM] = T[cid][cid] = cos_auto(alpha);
T[cid][DIM] = sin_auto(alpha);
T[DIM][cid] = -curvature() * sin_auto(alpha);
T[GDIM][GDIM] = T[cid][cid] = cos_auto(alpha);
T[cid][GDIM] = sin_auto(alpha);
T[GDIM][cid] = -curvature() * sin_auto(alpha);
return T;
}
@@ -311,14 +311,14 @@ transmatrix xpush(ld alpha) { return cpush(0, alpha); }
inline hyperpoint cpush0(int c, ld x) {
hyperpoint h = Hypc;
h[DIM] = cos_auto(x);
h[GDIM] = cos_auto(x);
h[c] = sin_auto(x);
return h;
}
inline hyperpoint xspinpush0(ld alpha, ld x) {
hyperpoint h = Hypc;
h[DIM] = cos_auto(x);
h[GDIM] = cos_auto(x);
h[0] = sin_auto(x) * cos(alpha);
h[1] = sin_auto(x) * -sin(alpha);
return h;
@@ -400,7 +400,7 @@ transmatrix rspintoc(const hyperpoint& H, int t, int f) {
// rotate the hyperbolic plane around C0 such that H[1] == 0 and H[0] >= 0
transmatrix spintox(const hyperpoint& H) {
if(DIM == 2) return spintoc(H, 0, 1);
if(GDIM == 2) return spintoc(H, 0, 1);
transmatrix T1 = spintoc(H, 0, 1);
return spintoc(T1*H, 0, 2) * T1;
}
@@ -421,7 +421,7 @@ transmatrix build_matrix(hyperpoint h1, hyperpoint h2, hyperpoint h3) {
// reverse of spintox(H)
transmatrix rspintox(const hyperpoint& H) {
if(DIM == 2) return rspintoc(H, 0, 1);
if(GDIM == 2) return rspintoc(H, 0, 1);
transmatrix T1 = spintoc(H, 0, 1);
return rspintoc(H, 0, 1) * rspintoc(T1*H, 0, 2);
}
@@ -429,16 +429,16 @@ transmatrix rspintox(const hyperpoint& H) {
// for H such that H[1] == 0, this matrix pushes H to C0
transmatrix pushxto0(const hyperpoint& H) {
transmatrix T = Id;
T[0][0] = +H[DIM]; T[0][DIM] = -H[0];
T[DIM][0] = curvature() * H[0]; T[DIM][DIM] = +H[DIM];
T[0][0] = +H[GDIM]; T[0][GDIM] = -H[0];
T[GDIM][0] = curvature() * H[0]; T[GDIM][GDIM] = +H[GDIM];
return T;
}
// reverse of pushxto0(H)
transmatrix rpushxto0(const hyperpoint& H) {
transmatrix T = Id;
T[0][0] = +H[DIM]; T[0][DIM] = H[0];
T[DIM][0] = -curvature() * H[0]; T[DIM][DIM] = +H[DIM];
T[0][0] = +H[GDIM]; T[0][GDIM] = H[0];
T[GDIM][0] = -curvature() * H[0]; T[GDIM][GDIM] = +H[GDIM];
return T;
}
@@ -448,16 +448,16 @@ transmatrix ggpushxto0(const hyperpoint& H, ld co) {
return eupush(co * H);
}
transmatrix res = Id;
if(sqhypot_d(DIM, H) < 1e-12) return res;
ld fac = (H[DIM]-1) / sqhypot_d(DIM, H);
for(int i=0; i<DIM; i++)
for(int j=0; j<DIM; j++)
if(sqhypot_d(GDIM, H) < 1e-12) return res;
ld fac = (H[GDIM]-1) / sqhypot_d(GDIM, H);
for(int i=0; i<GDIM; i++)
for(int j=0; j<GDIM; 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];
for(int d=0; d<GDIM; d++)
res[d][GDIM] = co * H[d],
res[GDIM][d] = -curvature() * co * H[d];
res[GDIM][GDIM] = H[GDIM];
return res;
}
@@ -476,16 +476,16 @@ transmatrix rgpushxto0(const hyperpoint& H) {
void fixmatrix(transmatrix& T) {
if(euclid) {
for(int x=0; x<DIM; x++) for(int y=0; y<=x; y++) {
for(int x=0; x<GDIM; x++) for(int y=0; y<=x; y++) {
ld dp = 0;
for(int z=0; z<DIM; z++) dp += T[z][x] * T[z][y];
for(int z=0; z<GDIM; z++) dp += T[z][x] * T[z][y];
if(y == x) dp = 1 - sqrt(1/dp);
for(int z=0; z<DIM; z++) T[z][x] -= dp * T[z][y];
for(int z=0; z<GDIM; z++) T[z][x] -= dp * T[z][y];
}
for(int x=0; x<DIM; x++) T[DIM][x] = 0;
T[DIM][DIM] = 1;
for(int x=0; x<GDIM; x++) T[GDIM][x] = 0;
T[GDIM][GDIM] = 1;
}
else for(int x=0; x<MDIM; x++) for(int y=0; y<=x; y++) {
ld dp = 0;
@@ -500,7 +500,7 @@ void fixmatrix(transmatrix& T) {
// show the matrix on screen
ld det(const transmatrix& T) {
if(DIM == 2) {
if(GDIM == 2) {
ld det = 0;
for(int i=0; i<3; i++)
det += T[0][i] * T[1][(i+1)%3] * T[2][(i+2)%3];
@@ -512,14 +512,14 @@ ld det(const transmatrix& T) {
ld det = 1;
transmatrix M = T;
for(int a=0; a<MDIM; a++) {
for(int b=a; b<=DIM; b++)
for(int b=a; b<=GDIM; 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++) {
for(int b=a+1; b<=GDIM; b++) {
ld co = -M[b][a] / M[a][a];
for(int c=a; c<MDIM; c++) M[b][c] += M[a][c] * co;
}
@@ -534,7 +534,7 @@ void inverse_error(const transmatrix& T) {
}
transmatrix inverse(const transmatrix& T) {
if(DIM == 2) {
if(GDIM == 2) {
ld d = det(T);
transmatrix T2;
if(d == 0) {
@@ -565,7 +565,7 @@ transmatrix inverse(const transmatrix& T) {
swap(T1[b][c], T1[a][c]), swap(T2[b][c], T2[a][c]);
if(!T1[a][a]) { inverse_error(T); return Id; }
for(int b=a+1; b<=DIM; b++) {
for(int b=a+1; b<=GDIM; 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;
}
@@ -587,13 +587,13 @@ transmatrix inverse(const transmatrix& T) {
ld hdist0(const hyperpoint& mh) {
switch(cgclass) {
case gcHyperbolic:
if(mh[DIM] < 1) return 0;
return acosh(mh[DIM]);
if(mh[GDIM] < 1) return 0;
return acosh(mh[GDIM]);
case gcEuclid: {
return hypot_d(DIM, mh);
return hypot_d(GDIM, mh);
}
case gcSphere: {
ld res = mh[DIM] >= 1 ? 0 : mh[DIM] <= -1 ? M_PI : acos(mh[DIM]);
ld res = mh[GDIM] >= 1 ? 0 : mh[GDIM] <= -1 ? M_PI : acos(mh[GDIM]);
if(elliptic && res > M_PI/2) res = M_PI-res;
return res;
}
@@ -634,7 +634,7 @@ ld hdist(const hyperpoint& h1, const hyperpoint& h2) {
}
hyperpoint mscale(const hyperpoint& t, double fac) {
if(DIM == 3) return cpush(2, fac) * t;
if(GDIM == 3) return cpush(2, fac) * t;
hyperpoint res;
for(int i=0; i<MDIM; i++)
res[i] = t[i] * fac;
@@ -642,7 +642,7 @@ hyperpoint mscale(const hyperpoint& t, double fac) {
}
transmatrix mscale(const transmatrix& t, double fac) {
if(DIM == 3) return t * cpush(2, fac);
if(GDIM == 3) return t * cpush(2, fac);
transmatrix res;
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
res[i][j] = t[i][j] * fac;
@@ -651,24 +651,24 @@ transmatrix mscale(const transmatrix& t, double fac) {
transmatrix xyscale(const transmatrix& t, double fac) {
transmatrix res;
for(int i=0; i<MDIM; i++) for(int j=0; j<DIM; j++)
for(int i=0; i<MDIM; i++) for(int j=0; j<GDIM; 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<MDIM; i++) for(int j=0; j<DIM; j++)
for(int i=0; i<MDIM; i++) for(int j=0; j<GDIM; j++)
res[i][j] = t[i][j] * fac;
for(int i=0; i<MDIM; i++)
res[i][DIM] = t[i][DIM] * facz;
res[i][GDIM] = t[i][GDIM] * facz;
return res;
}
// double downspin_zivory;
transmatrix mzscale(const transmatrix& t, double fac) {
if(DIM == 3) return t * cpush(2, fac);
if(GDIM == 3) return t * cpush(2, fac);
// take only the spin
transmatrix tcentered = gpushxto0(tC0(t)) * t;
// tcentered = tcentered * spin(downspin_zivory);