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ellipse approximation calculations

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This commit is contained in:
Florian Stecker 2022-03-21 18:31:59 -04:00
parent ca8799702d
commit d71b1b9507
5 changed files with 423 additions and 260 deletions
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621
draw.c
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@ -29,6 +29,43 @@ double scal(vector_t a, vector_t b)
return result; return result;
} }
// degenerate conic whose zero set is the union of two lines
// Q = a^T b + b^T a
void degenerate_conic(vector_t a, vector_t b, gsl_matrix *conic)
{
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j, a.x[i]*b.x[j] + a.x[j]*b.x[i]);
}
double conic_value(gsl_matrix *conic, vector_t v)
{
double result = 0.0;
LOOP(i) LOOP(j) result += gsl_matrix_get(conic, i, j) * v.x[i] * v.x[j];
return result;
}
// finds conic in the pencil through (l1,l2) and (L1,L2) going through p
void conic_from_lines(workspace_t *ws, vector_t l1, vector_t l2, vector_t L1, vector_t L2, vector_t p, gsl_matrix *conic)
{
gsl_matrix *degenerate1 = gsl_matrix_alloc(3, 3);
gsl_matrix *degenerate2 = gsl_matrix_alloc(3, 3);
gsl_matrix *tmp = gsl_matrix_alloc(3, 3);
degenerate_conic(l1, l2, degenerate1);
degenerate_conic(L1, L2, degenerate2);
double t = - conic_value(degenerate1, p) / conic_value(degenerate2, p);
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j,
gsl_matrix_get(degenerate1, i, j) +
gsl_matrix_get(degenerate2, i, j)*t);
int positives = diagonalize_symmetric_form(conic, tmp, ws);
if(positives == 2)
LOOP(i) LOOP(j) *gsl_matrix_ptr(conic, i, j) *= -1;
gsl_matrix_free(degenerate1);
gsl_matrix_free(degenerate2);
gsl_matrix_free(tmp);
}
vector_t apply(gsl_matrix *m, vector_t x) vector_t apply(gsl_matrix *m, vector_t x)
{ {
vector_t out; vector_t out;
@ -49,7 +86,7 @@ vector_t apply_transpose(gsl_matrix *m, vector_t x)
return out; return out;
} }
vector_t apply_inverse(gsl_matrix *m, vector_t in) vector_t apply_pseudoinverse_transpose(gsl_matrix *m, vector_t in)
{ {
vector_t out; vector_t out;
double cofactor; double cofactor;
@ -64,6 +101,80 @@ vector_t apply_inverse(gsl_matrix *m, vector_t in)
return out; return out;
} }
vector_t apply_pseudoinverse(gsl_matrix *m, vector_t in)
{
vector_t out;
double cofactor;
LOOP(i) out.x[i] = 0.0;
LOOP(i) LOOP(j) {
cofactor = gsl_matrix_get(m, (j+1)%3, (i+1)%3) * gsl_matrix_get(m, (j+2)%3, (i+2)%3)
- gsl_matrix_get(m, (j+1)%3, (i+2)%3) * gsl_matrix_get(m, (j+2)%3, (i+1)%3);
out.x[i] += cofactor * in.x[j];
}
return out;
}
int intersect_line_and_conic(DrawingContext *ctx, vector_t line, gsl_matrix *conic, vector_t *intersection1, vector_t *intersection2)
{
gsl_matrix *frame = getTempMatrix(ctx->ws);
int pos = diagonalize_symmetric_form(conic, frame, ctx->ws);
vector_t a = apply_pseudoinverse_transpose(frame, line);
double disc = a.x[0]*a.x[0] + a.x[1]*a.x[1] - a.x[2]*a.x[2];
if(disc < 0)
{
return 0;
}
vector_t intersection1_in_frame;
intersection1_in_frame.x[0] = -a.x[0]*a.x[2] + a.x[1]*sqrt(disc);
intersection1_in_frame.x[1] = -a.x[1]*a.x[2] - a.x[0]*sqrt(disc);
intersection1_in_frame.x[2] = a.x[0]*a.x[0] + a.x[1]*a.x[1];
*intersection1 = apply_pseudoinverse(frame, intersection1_in_frame);
vector_t intersection2_in_frame;
intersection2_in_frame.x[0] = -a.x[0]*a.x[2] - a.x[1]*sqrt(disc);
intersection2_in_frame.x[1] = -a.x[1]*a.x[2] + a.x[0]*sqrt(disc);
intersection2_in_frame.x[2] = a.x[0]*a.x[0] + a.x[1]*a.x[1];
*intersection2 = apply_pseudoinverse(frame, intersection2_in_frame);
releaseTempMatrices(ctx->ws, 1);
}
// should be three collinear vectors!
double halfCR(vector_t x, vector_t y, vector_t z)
{
double xy = scal(x,y);
double yz = scal(y,z);
double zx = scal(z,x);
double yy = scal(y,y);
double xx = scal(x,x);
return fabs((yz*xy-zx*yy)/(yz*xx-zx*xy));
}
void getMinMaxHalfCrossRatio(double *limit_curve, int n, vector_t v1, vector_t v2, int max, int *min_index, double* min_cr)
{
vector_t fp[3];
vector_t tangent;
double cr;
*min_cr = max ? 0 : INFINITY;
for(int i = 0; i < n; i++) {
LOOP(j) LOOP(k) fp[j].x[k] = limit_curve[12*i+3+3*j+k];
tangent = cross(fp[0],fp[1]);
cr = fabs(scal(v2, tangent) / scal(v1, tangent));
if(!max && cr < *min_cr || max && cr > *min_cr) {
*min_cr = cr;
*min_index = i;
}
}
}
int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out) int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
{ {
gsl_matrix *tmp = getTempMatrix(ctx->ws); gsl_matrix *tmp = getTempMatrix(ctx->ws);
@ -389,6 +500,28 @@ void drawRotationOrbitFrame(DrawingContext *ctx, gsl_matrix *frame, vector_t sta
releaseTempVectors(ctx->ws, 2); releaseTempVectors(ctx->ws, 2);
} }
void drawConic(DrawingContext *ctx, gsl_matrix *form)
{
gsl_matrix *orthogonal_frame = getTempMatrix(ctx->ws);
gsl_matrix *frame = getTempMatrix(ctx->ws);
double eval[3];
vector_t start;
diagonalize_symmetric_matrix(form, orthogonal_frame, eval, ctx->ws);
LOOP(i) LOOP(j)
gsl_matrix_set(frame, j, i,
gsl_matrix_get(orthogonal_frame, i, j)/sqrt(fabs(eval[i])));
// find any timelike vector; a simple method is adding the first and third column of frame
LOOP(i) start.x[i] = gsl_matrix_get(frame, i, 0) + gsl_matrix_get(frame, i, 2);
drawRotationOrbitFrame(ctx, frame, start);
releaseTempMatrices(ctx->ws, 2);
}
void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start) void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
{ {
gsl_matrix *frame = getTempMatrix(ctx->ws); gsl_matrix *frame = getTempMatrix(ctx->ws);
@ -609,15 +742,19 @@ void drawAttractors(DrawingContext *ctx)
for(int i = 0; i < n; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]); for(int i = 0; i < n; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
for(int i = 0; i < n; i++) LOOP(j) { for(int i = 0; i < n; i++) {
for(int j = 0; j < 3; j += 1) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]); cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawVector(ctx, p[i][j]); drawVector(ctx, p[i][j]);
} }
}
for(int i = 0; i < n; i++) LOOP(j) { for(int i = 0; i < n; i++) {
for(int j = 0; j < 3; j += 1) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]); cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawCovector(ctx, l[i][j]); drawCovector(ctx, l[i][j]);
} }
}
} }
char *conjugate_word(const char *word, int modifier, const char *conj, char *buffer) char *conjugate_word(const char *word, int modifier, const char *conj, char *buffer)
@ -732,6 +869,10 @@ void drawBoxes(DrawingContext *ctx)
{ {
gsl_matrix *rot = getTempMatrix(ctx->ws); gsl_matrix *rot = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3); gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix *order3 = getTempMatrix(ctx->ws);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *tmp2 = getTempMatrix(ctx->ws);
gsl_matrix *conic = getTempMatrix(ctx->ws);
gsl_matrix *frame = getTempMatrix(ctx->ws); gsl_matrix *frame = getTempMatrix(ctx->ws);
cairo_t *C = ctx->cairo; cairo_t *C = ctx->cairo;
cairo_save(C); cairo_save(C);
@ -751,180 +892,95 @@ void drawBoxes(DrawingContext *ctx)
cairo_set_line_width(C, 2.0/ctx->dim->scalefactor); cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
cairo_set_source_rgb(C, 0.6, 0.6, 0.6); cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
drawRotationOrbit(ctx, "ab", p[0][0]); // drawRotationOrbit(ctx, "ab", p[0][0]);
drawRotationOrbit(ctx, "bc", p[0][0]);
drawRotationOrbit(ctx, "ca", p[0][0]);
if(ctx->mode >= 2) {
cairo_set_source_rgb(C, 0.6, 0.6, 1);
drawRotationOrbit(ctx, "bcabcb", p[1][0]); // bcC
drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abcC
// drawRotationOrbit(ctx, "bcabcabacb", p[1][0]); // bcabC''
// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // bacaC'
// drawRotationOrbit(ctx, "bcacabcacacb", p[4][0]); // bcacaC' bcacabacb
}
cairo_set_source_rgb(C, 1, 0, 1);
// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // ababcba
cairo_set_source_rgb(C, 0, 0, 0);
fixedPoints(ctx, "abababcbaba", p[3]);
// drawRotationOrbit(ctx, "abababcabcbababa", p[3][0]); // bab abc bab
cairo_set_source_rgb(C, 0, 0, 1);
// fixedPoints(ctx, "cab", p[3]);
// drawRotationOrbit(ctx, "cabc", p[3][0]);
// fixedPoints(ctx, "bca", p[3]);
// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
// fixedPoints(ctx, "bc abc cb", p[3]);
// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
fixedPoints(ctx, "bc bca cb", p[3]);
// drawRotationOrbit(ctx, "bcbcacbc", p[3][0]);
/*
cairo_set_source_rgb(C, 0, 0, 0);
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ab", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
// drawVector(ctx, ptmp[2]);
}
strncpy(word,"bca",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ab", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
// drawVector(ctx, ptmp[2]);
}
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "bc", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"cab",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "bc", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"cab",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ca", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ca", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
*/
/*
cairo_set_source_rgb(C, 1, 0, 0);
drawVector(ctx, p[0][0]);
cairo_set_source_rgb(C, 0, 0.6, 0);
drawVector(ctx, p[1][0]);
cairo_set_source_rgb(C, 0, 0, 1);
drawVector(ctx, p[2][0]);
*/
/*
fixedPoints(ctx, "ab abc ba", p[4]);
fixedPoints(ctx, "abab abc baba", p[5]);
fixedPoints(ctx, "ababab abc bababa", p[6]);
fixedPoints(ctx, "abababab abc babababa", p[7]);
fixedPoints(ctx, "babababa abc abababab", p[8]);
fixedPoints(ctx, "bababa abc ababab", p[9]);
fixedPoints(ctx, "baba abc abab", p[10]);
fixedPoints(ctx, "ba abc ab", p[11]);
fixedPoints(ctx, "bca", p[12]);
fixedPoints(ctx, "b abc b", p[13]);
fixedPoints(ctx, "bab abc bab", p[14]);
fixedPoints(ctx, "babab abc babab", p[15]);
fixedPoints(ctx, "bababab abc bababab", p[16]);
fixedPoints(ctx, "abababab bca babababa", p[17]);
fixedPoints(ctx, "ababab bca bababa", p[18]);
fixedPoints(ctx, "abab bca baba", p[19]);
fixedPoints(ctx, "ab bca ba", p[20]);
*/
// initializeTriangleGenerators(gen, ctx->cartan);
// for(int i = 0; i < 22; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
// LOOP(i) LOOP(j) alpha[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
/*
gsl_matrix_set(frame, 0, 0, 2.0);
gsl_matrix_set(frame, 0, 1, 0.0);
gsl_matrix_set(frame, 0, 2, 1.0);
gsl_matrix_set(frame, 1, 0, -1.0);
gsl_matrix_set(frame, 1, 1, sqrt(3));
gsl_matrix_set(frame, 1, 2, 1.0);
gsl_matrix_set(frame, 2, 0, -1.0);
gsl_matrix_set(frame, 2, 1, -sqrt(3));
gsl_matrix_set(frame, 2, 2, 1.0);*/
// drawRotationOrbitFrame(ctx, frame, p[0][0]);
// drawRotationOrbit(ctx, "bc", p[0][0]); // drawRotationOrbit(ctx, "bc", p[0][0]);
// drawRotationOrbit(ctx, "ca", p[0][0]); // drawRotationOrbit(ctx, "ca", p[0][0]);
/* // drawRotationOrbit(ctx, "ab", p[0][2]);
for(int i = 0; i < 18; i++) { // drawRotationOrbit(ctx, "bc", p[0][2]);
if(i == 0) // drawRotationOrbit(ctx, "ca", p[0][2]);
cairo_set_source_rgb(C, 1, 0, 0);
else if(i == 8)
cairo_set_source_rgb(C, 0, 0, 1);
else if(i == 9)
cairo_set_source_rgb(C, 0, 0.6, 0);
else
cairo_set_source_rgb(C, 0, 0, 0);
drawVector(ctx, p[3+i][0]);
// drawCovector(ctx, l[3+i][0]);
}
*/
// drawRotationOrbit(ctx, "ab", cross(l[0][0], l[2][1])); // gsl_matrix_set_zero(order3);
// LOOP(i) gsl_matrix_set(order3, (i+1)%3, i, 1);
// rotation_frame(order3, frame, ctx->ws);
// drawRotationOrbitFrame(ctx, frame, p[0][0]);
// drawRotationOrbitFrame(ctx, frame, p[0][2]);
// drawRotationOrbit(ctx, "abca", p[0][0]); vector_t line1;
vector_t line2;
double t;
int positives;
/*
// conic 1
line1 = cross(p[0][0],p[0][1]);
line2 = cross(p[1][0],p[1][1]);
degenerate_conic(line1, line2, tmp);
line1 = cross(p[0][0], p[1][0]);
line2 = cross(p[0][0], p[1][0]);
degenerate_conic(line1, line2, tmp2);
t = - conic_value(tmp, p[2][0]) / conic_value(tmp2, p[2][0]);
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j,
gsl_matrix_get(tmp, i, j) +
gsl_matrix_get(tmp2, i, j)*t);
positives = diagonalize_symmetric_form(conic, tmp, ctx->ws);
if(positives == 2)
LOOP(i) LOOP(j) *gsl_matrix_ptr(conic, i, j) *= -1;
drawConic(ctx, conic);
*/
// conic 2
line1 = cross(p[0][0],p[0][1]);
line2 = cross(p[2][0],p[2][1]);
degenerate_conic(line1, line2, tmp);
line1 = cross(p[0][0], p[2][0]);
line2 = cross(p[0][0], p[2][0]);
degenerate_conic(line1, line2, tmp2);
t = - conic_value(tmp, p[1][0]) / conic_value(tmp2, p[1][0]);
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j,
gsl_matrix_get(tmp, i, j) +
gsl_matrix_get(tmp2, i, j)*t);
positives = diagonalize_symmetric_form(conic, tmp, ctx->ws);
if(positives == 2)
LOOP(i) LOOP(j) *gsl_matrix_ptr(conic, i, j) *= -1;
drawConic(ctx, conic);
/*
// conic 3
line1 = cross(p[0][2],p[0][1]);
line2 = cross(p[1][2],p[1][1]);
degenerate_conic(line1, line2, tmp);
line1 = cross(p[0][2], p[1][2]);
line2 = cross(p[0][2], p[1][2]);
degenerate_conic(line1, line2, tmp2);
t = - conic_value(tmp, p[2][2]) / conic_value(tmp2, p[2][2]);
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j,
gsl_matrix_get(tmp, i, j) +
gsl_matrix_get(tmp2, i, j)*t);
positives = diagonalize_symmetric_form(conic, tmp, ctx->ws);
if(positives == 2)
LOOP(i) LOOP(j) *gsl_matrix_ptr(conic, i, j) *= -1;
drawConic(ctx, conic);
*/
// conic 4
line1 = cross(p[0][2],p[0][1]);
line2 = cross(p[2][2],p[2][1]);
degenerate_conic(line1, line2, tmp);
line1 = cross(p[0][2], p[2][2]);
line2 = cross(p[0][2], p[2][2]);
degenerate_conic(line1, line2, tmp2);
t = - conic_value(tmp, p[1][2]) / conic_value(tmp2, p[1][2]);
LOOP(i) LOOP(j) gsl_matrix_set(conic, i, j,
gsl_matrix_get(tmp, i, j) +
gsl_matrix_get(tmp2, i, j)*t);
positives = diagonalize_symmetric_form(conic, tmp, ctx->ws);
if(positives == 2)
LOOP(i) LOOP(j) *gsl_matrix_ptr(conic, i, j) *= -1;
drawConic(ctx, conic);
cairo_restore(C); cairo_restore(C);
releaseTempMatrices(ctx->ws, 5); releaseTempMatrices(ctx->ws, 9);
}
void getMinMaxHalfCrossRatio(double *limit_curve, int n, vector_t v1, vector_t v2, int max, int *min_index, double* min_cr)
{
vector_t fp[3];
vector_t tangent;
double cr;
*min_cr = max ? 0 : INFINITY;
for(int i = 0; i < n; i++) {
LOOP(j) LOOP(k) fp[j].x[k] = limit_curve[12*i+3+3*j+k];
tangent = cross(fp[0],fp[1]);
cr = fabs(scal(v1, tangent) / scal(v2, tangent));
if(!max && cr < *min_cr || max && cr > *min_cr) {
*min_cr = cr;
*min_index = i;
}
}
} }
void drawBoxes2(DrawingContext *ctx) void drawBoxes2(DrawingContext *ctx)
@ -933,104 +989,173 @@ void drawBoxes2(DrawingContext *ctx)
gsl_matrix **gen = getTempMatrices(ctx->ws, 3); gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_vector *marking_globalbasis = getTempVector(ctx->ws); gsl_vector *marking_globalbasis = getTempVector(ctx->ws);
gsl_vector *marking_drawbasis = getTempVector(ctx->ws); gsl_vector *marking_drawbasis = getTempVector(ctx->ws);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *tmp2 = getTempMatrix(ctx->ws);
gsl_matrix *conic = getTempMatrix(ctx->ws);
cairo_t *C = ctx->cairo; cairo_t *C = ctx->cairo;
cairo_save(C); cairo_save(C);
initializeTriangleGenerators(gen, ctx->cartan); initializeTriangleGenerators(gen, ctx->cartan);
vector_t p[4][3]; vector_t p[3][3];
cairo_set_line_width(C, 1/ctx->dim->scalefactor);
cairo_set_source_rgb(C, 0, 0, 0);
// find coxeter fixed points and triangle vertices
fixedPoints(ctx, "abc", p[0]); fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]); fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]); fixedPoints(ctx, "cab", p[2]);
cairo_set_line_width(C, 1/ctx->dim->scalefactor);
cairo_set_source_rgb(C, 0, 0, 0);
vector_t att_line[3];
vector_t rep_line[3];
LOOP(i) att_line[i] = cross(p[i][0], p[i][1]);
LOOP(i) rep_line[i] = cross(p[i][2], p[i][1]);
vector_t vertex[3]; vector_t vertex[3];
LOOP(i) vertex[i] = cross( LOOP(i) vertex[i] = cross(
cross(p[(i+1)%3][0],p[(i+1)%3][2]), cross(p[(i+1)%3][0],p[(i+1)%3][2]),
cross(p[(i+2)%3][0],p[(i+2)%3][2])); cross(p[(i+2)%3][0],p[(i+2)%3][2]));
vector_t a,b;
double t = ctx->distance_parameter1, s = ctx->distance_parameter2;
vector_t phiplus, phiminus, eta;
double dvert, param;
// want to choose a so that d(vertex[0],a) = t*d(vertex[0],vertex[1])
phiplus = cross(p[2][0], p[2][1]);
phiminus = cross(p[2][2], p[2][1]);
dvert = log(
(scal(phiplus, vertex[0])*scal(phiminus, vertex[1])) /
(scal(phiplus, vertex[1])*scal(phiminus, vertex[0])));
LOOP(i) eta.x[i] =
scal(phiminus, vertex[0]) / scal(phiplus, vertex[0])
* exp(t*dvert) * phiplus.x[i]
- phiminus.x[i];
param = 1/(1-scal(eta,vertex[0])/scal(eta,vertex[1]));
LOOP(i) a.x[i] = param*vertex[0].x[i] + (1-param)*vertex[1].x[i];
// want to choose b so that d(vertex[0],b) = s*d(vertex[0],vertex[2])
phiplus = cross(p[1][0], p[1][1]);
phiminus = cross(p[1][2], p[1][1]);
dvert = log(
(scal(phiplus, vertex[0])*scal(phiminus, vertex[2])) /
(scal(phiplus, vertex[2])*scal(phiminus, vertex[0])));
LOOP(i) eta.x[i] =
scal(phiminus, vertex[0]) / scal(phiplus, vertex[0])
* exp(s*dvert) * phiplus.x[i]
- phiminus.x[i];
param = 1/(1-scal(eta,vertex[0])/scal(eta,vertex[2]));
LOOP(i) b.x[i] = param*vertex[0].x[i] + (1-param)*vertex[2].x[i];
// draw and output stuff
LOOP(i) drawVector(ctx, vertex[i]); LOOP(i) drawVector(ctx, vertex[i]);
// LOOP(i) drawCovector(ctx, att_line[i]); drawVector(ctx, a);
drawVector(ctx, b);
drawCovector(ctx, cross(a,b));
drawCovector(ctx, cross(b,vertex[0]));
drawCovector(ctx, cross(vertex[0],a));
double half_cross_ratio[3]; // find the intersections with the limit set and the asymmetric distances
LOOP(i) half_cross_ratio[i] = scal(vertex[(i+1)%3],att_line[i])/scal(vertex[(i+2)%3],att_line[i]); int boundary_index;
double triple_ratio = half_cross_ratio[0]*half_cross_ratio[1]*half_cross_ratio[2]; double value;
LOOP(i) half_cross_ratio[i] = scal(vertex[(i+1)%3],rep_line[i])/scal(vertex[(i+2)%3],rep_line[i]); double perimeter1 = 0.0, perimeter2 = 0.0;
double triple_ratio2 = half_cross_ratio[0]*half_cross_ratio[1]*half_cross_ratio[2]; double approx_perimeter1 = 0.0, approx_perimeter2 = 0.0;
vector_t boundary_point;
cairo_set_source_rgb(C, 1, 0, 0);
vector_t marking, marking2, marking3;
gsl_vector_set(marking_drawbasis, 0, ctx->marking.x);
gsl_vector_set(marking_drawbasis, 1, ctx->marking.y);
gsl_vector_set(marking_drawbasis, 2, 1);
solve(ctx->cob, marking_drawbasis, marking_globalbasis, ctx->ws);
LOOP(i) marking.x[i] = gsl_vector_get(marking_globalbasis, i);
gsl_vector_set(marking_drawbasis, 0, ctx->marking2.x);
gsl_vector_set(marking_drawbasis, 1, ctx->marking2.y);
gsl_vector_set(marking_drawbasis, 2, 1);
solve(ctx->cob, marking_drawbasis, marking_globalbasis, ctx->ws);
LOOP(i) marking2.x[i] = gsl_vector_get(marking_globalbasis, i);
gsl_vector_set(marking_drawbasis, 0, ctx->marking3.x);
gsl_vector_set(marking_drawbasis, 1, ctx->marking3.y);
gsl_vector_set(marking_drawbasis, 2, 1);
solve(ctx->cob, marking_drawbasis, marking_globalbasis, ctx->ws);
LOOP(i) marking3.x[i] = gsl_vector_get(marking_globalbasis, i);
/*
vector_t line_drawbasis = apply_inverse(ctx->cob, cross(marking, vertex[0]));
double last, current;
int boundary_points[2] = {0,0};
int current_boundary_point = 0;
last =
ctx->limit_curve[12*(ctx->n_group_elements-1) ]*line_drawbasis.x[0] +
ctx->limit_curve[12*(ctx->n_group_elements-1)+1]*line_drawbasis.x[1] +
line_drawbasis.x[2];
*/
double value[6];
int boundary_point[6];
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements, getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
marking, marking2, 1, &boundary_point[0], &value[0]); a, b, 1, &boundary_index, &value);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements, LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
marking2, marking3, 1, &boundary_point[1], &value[1]); drawVector(ctx, boundary_point);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements, perimeter1 += log(value);
marking3, marking, 1, &boundary_point[2], &value[2]);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
marking, marking2, 0, &boundary_point[0], &value[3]);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
marking2, marking3, 0, &boundary_point[1], &value[4]);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
marking3, marking, 0, &boundary_point[2], &value[5]);
/* vector_t fp[3], tangent; getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
LOOP(j) LOOP(k) fp[j].x[k] = ctx->limit_curve[12*boundary_point[0]+3+3*j+k]; b, vertex[0], 1, &boundary_index, &value);
tangent = cross(fp[0],fp[1]); LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
drawCovector(ctx, tangent);*/ drawVector(ctx, boundary_point);
perimeter1 += log(value);
approx_perimeter1 += log(value);
snprintf(ctx->extra_text, 1000, "tr1 = %f, tr2 2 = %f, aa = %f", getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
log(value[0])+log(value[1])+log(value[2]), vertex[0], a, 1, &boundary_index, &value);
-log(value[3])-log(value[4])-log(value[5]), LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
log(value[0])+log(value[1])+log(value[2])+log(value[3])+log(value[4])+log(value[5])); drawVector(ctx, boundary_point);
perimeter1 += log(value);
approx_perimeter1 += log(value);
drawCovector(ctx, cross(marking, marking2)); cairo_set_source_rgb(C, 0, 0, 1);
drawCovector(ctx, cross(marking2, marking3));
drawCovector(ctx, cross(marking3, marking)); getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
b, a, 1, &boundary_index, &value);
LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
drawVector(ctx, boundary_point);
perimeter2 += log(value);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
vertex[0], b, 1, &boundary_index, &value);
LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
drawVector(ctx, boundary_point);
perimeter2 += log(value);
approx_perimeter2 += log(value);
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
a, vertex[0], 1, &boundary_index, &value);
LOOP(k) boundary_point.x[k] = ctx->limit_curve[12*boundary_index+3+k];
drawVector(ctx, boundary_point);
perimeter2 += log(value);
approx_perimeter2 += log(value);
vector_t conic_intersection[2];
double hC0, hC1;
// find the outer conic
cairo_set_source_rgb(C, 0, 0.7, 0);
conic_from_lines(ctx->ws,
cross(p[0][0], p[0][1]), cross(p[1][0], p[1][1]),
cross(p[0][0], p[1][0]), cross(p[0][0], p[1][0]),
p[2][0], conic);
drawConic(ctx, conic);
conic_intersection[2];
intersect_line_and_conic(ctx, cross(a, b), conic,
&conic_intersection[0], &conic_intersection[1]);
hC0 = halfCR(b, a, conic_intersection[0]);
hC1 = halfCR(b, a, conic_intersection[1]);
if(hC0 > hC1)
drawVector(ctx, conic_intersection[0]);
else
drawVector(ctx, conic_intersection[1]);
approx_perimeter2 += log(hC0 > hC1 ? hC0 : hC1);
// find the inner conic
cairo_set_source_rgb(C, 0, 0.5, 0.5);
conic_from_lines(ctx->ws,
cross(p[0][2], p[0][1]), cross(p[1][2], p[1][1]),
cross(p[0][2], p[1][2]), cross(p[0][2], p[1][2]),
p[2][2], conic);
drawConic(ctx, conic);
conic_intersection[2];
intersect_line_and_conic(ctx, cross(a, b), conic,
&conic_intersection[0], &conic_intersection[1]);
hC0 = halfCR(a, b, conic_intersection[0]);
hC1 = halfCR(a, b, conic_intersection[1]);
if(hC0 > hC1)
drawVector(ctx, conic_intersection[0]);
else
drawVector(ctx, conic_intersection[1]);
approx_perimeter1 += log(hC0 > hC1 ? hC0 : hC1);
// output
snprintf(ctx->extra_text, 1000, "perimeter1 = %f (%f), perimeter2 = %f (%f)",
perimeter1, approx_perimeter1,
perimeter2, approx_perimeter2);
printf("%f %f %f %f %f %f\n",
t, s, perimeter1, perimeter2, approx_perimeter1, approx_perimeter2);
cairo_restore(C); cairo_restore(C);
releaseTempMatrices(ctx->ws, 4); releaseTempMatrices(ctx->ws, 7);
releaseTempVectors(ctx->ws, 2); releaseTempVectors(ctx->ws, 2);
} }
@ -1341,9 +1466,9 @@ void draw(DrawingContext *ctx)
if(ctx->show_marking) if(ctx->show_marking)
{ {
cairo_set_source_rgb(C, 0, 0, 1); cairo_set_source_rgb(C, 0, 0, 1);
drawPoint(ctx, ctx->marking); // drawPoint(ctx, ctx->marking);
drawPoint(ctx, ctx->marking2); // drawPoint(ctx, ctx->marking2);
drawPoint(ctx, ctx->marking3); // drawPoint(ctx, ctx->marking3);
} }
if(ctx->show_coxeter_orbit) if(ctx->show_coxeter_orbit)

27
linalg.c
View File

@ -315,7 +315,6 @@ int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws)
ERROR(r, "gsl_eigen_symmv failed!\n"); ERROR(r, "gsl_eigen_symmv failed!\n");
gsl_eigen_symmv_sort(ws->eval_real, cob, GSL_EIGEN_SORT_VAL_ASC); gsl_eigen_symmv_sort(ws->eval_real, cob, GSL_EIGEN_SORT_VAL_ASC);
gsl_matrix_transpose(cob); gsl_matrix_transpose(cob);
int positive = 0; int positive = 0;
@ -332,6 +331,32 @@ int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws)
return positive; return positive;
} }
int diagonalize_symmetric_matrix(gsl_matrix *A, gsl_matrix *cob, double *eval, workspace_t *ws)
{
gsl_matrix *A_ = getTempMatrix(ws);
gsl_matrix_memcpy(A_, A);
int r = gsl_eigen_symmv (A_, ws->eval_real, cob, ws->work_symmv);
ERROR(r, "gsl_eigen_symmv failed!\n");
gsl_eigen_symmv_sort(ws->eval_real, cob, GSL_EIGEN_SORT_VAL_ASC);
gsl_matrix_transpose(cob);
int positive = 0;
for(int i = 0; i < ws->n; i++) {
if(eval)
eval[i] = gsl_vector_get(ws->eval_real, i);
if(gsl_vector_get(ws->eval_real, i) > 0)
positive++;
}
releaseTempMatrices(ws, 1);
return positive;
}
// computes a matrix in SL(3, R) which projectively transforms (e1, e2, e3, e1+e2+e3) to the 4 given vectors // computes a matrix in SL(3, R) which projectively transforms (e1, e2, e3, e1+e2+e3) to the 4 given vectors
void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws) void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws)
{ {

1
linalg.h
View File

@ -53,6 +53,7 @@ int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
int real_eigenvalues(gsl_matrix *g, gsl_vector *evec, workspace_t *ws); int real_eigenvalues(gsl_matrix *g, gsl_vector *evec, workspace_t *ws);
void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws); void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws);
int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws); int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws);
int diagonalize_symmetric_matrix(gsl_matrix *A, gsl_matrix *cob, double *eval, workspace_t *ws);
void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws); void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws);
void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws); void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws);

24
main.c
View File

@ -49,6 +49,8 @@ void setupContext(DrawingContext *ctx, int argc, char *argv[])
ctx->marking2.y = -0.11873; ctx->marking2.y = -0.11873;
ctx->marking3.x = -0.73679; ctx->marking3.x = -0.73679;
ctx->marking3.y = -0.21873; ctx->marking3.y = -0.21873;
ctx->distance_parameter1 = 0.95;
ctx->distance_parameter2 = 0.95;
ctx->show_coxeter_orbit = 0; ctx->show_coxeter_orbit = 0;
ctx->extra_text = malloc(1000*sizeof(char)); ctx->extra_text = malloc(1000*sizeof(char));
memset(ctx->extra_text, 0, 1000*sizeof(char)); memset(ctx->extra_text, 0, 1000*sizeof(char));
@ -77,17 +79,15 @@ void destroyContext(DrawingContext *ctx)
workspace_free(ctx->ws); workspace_free(ctx->ws);
} }
void computeRotationMatrix(DrawingContext *ctx, gsl_matrix *result, const char *type) void computeRotationMatrix(DrawingContext *ctx, gsl_matrix *result, const char *word)
{ {
gsl_matrix *tmp = getTempMatrix(ctx->ws); gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3); gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
// ERROR(strlen(type) != 2, "Invalid call of computeRotationMatrix()\n");
initializeTriangleGenerators(gen, ctx->cartan); initializeTriangleGenerators(gen, ctx->cartan);
gsl_matrix_set_identity(tmp); gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(type); i++) for(int i = 0; i < strlen(word); i++)
multiply_right(tmp, gen[type[i]-'a'], ctx->ws); multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
rotation_frame(tmp, result, ctx->ws); rotation_frame(tmp, result, ctx->ws);
@ -268,7 +268,7 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
case KeyPress: case KeyPress:
state = ev->xkey.state & (ShiftMask | LockMask | ControlMask); state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask)); key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask));
printf("Key pressed: %ld\n", key); // printf("Key pressed: %ld\n", key);
switch(key) { switch(key) {
case XK_Down: case XK_Down:
@ -355,6 +355,16 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
case 'p': case 'p':
print(screen_context); print(screen_context);
break; break;
case 'P':
for(int i = 0; i <= 100; i++) {
for(int j = 0; j <= 100; j++) {
screen_context->distance_parameter1 = 0.02*i;
screen_context->distance_parameter2 = 0.02*j;
draw(screen_context);
}
fflush(stdout);
}
break;
case 'M': case 'M':
/* /*
screen_context->limit_with_lines = 0; screen_context->limit_with_lines = 0;
@ -468,7 +478,7 @@ int main(int argc, char *argv[])
gettimeofday(&current_time, 0); gettimeofday(&current_time, 0);
end_time = current_time.tv_sec + current_time.tv_usec*1e-6; end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000); // printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000);
} }
waitUpdateTimer(info); waitUpdateTimer(info);
} }

2
main.h
View File

@ -46,6 +46,8 @@ typedef struct {
point_t marking; point_t marking;
point_t marking2; point_t marking2;
point_t marking3; point_t marking3;
double distance_parameter1;
double distance_parameter2;
int show_coxeter_orbit; int show_coxeter_orbit;
int use_repelling; int use_repelling;
gsl_matrix *cartan, *cob; gsl_matrix *cartan, *cob;