1360 lines
39 KiB
C
1360 lines
39 KiB
C
#include "main.h"
|
|
|
|
#define FMOD(x,y) (fmod(x,y) < 0 ? fmod(x,y) + y : fmod(x,y))
|
|
#define ANGLE_DIFF(x,y) (FMOD((x)-(y), 2*M_PI))
|
|
#define ANGLE_IN_INTERVAL(a,b,x) (ANGLE_DIFF(x,a) < ANGLE_DIFF(b,a))
|
|
#define FLIP(x,y) do {double tmp = x; x = y; y = tmp;} while(0)
|
|
|
|
// level 0: helper functions
|
|
|
|
int isInsideBB(DrawingContext *ctx, point_t p)
|
|
{
|
|
cairo_user_to_device(ctx->cairo, &p.x, &p.y);
|
|
return -p.x < ctx->dim->width && p.x < 3*ctx->dim->width && -p.y < ctx->dim->height && p.y < 3*ctx->dim->height;
|
|
}
|
|
|
|
vector_t cross(vector_t a, vector_t b)
|
|
{
|
|
vector_t result;
|
|
result.x[0] = a.x[1]*b.x[2] - a.x[2]*b.x[1];
|
|
result.x[1] = a.x[2]*b.x[0] - a.x[0]*b.x[2];
|
|
result.x[2] = a.x[0]*b.x[1] - a.x[1]*b.x[0];
|
|
return result;
|
|
}
|
|
|
|
double scal(vector_t a, vector_t b)
|
|
{
|
|
double result = 0.0;
|
|
LOOP(i) result += a.x[i]*b.x[i];
|
|
return result;
|
|
}
|
|
|
|
vector_t apply(gsl_matrix *m, vector_t x)
|
|
{
|
|
vector_t out;
|
|
|
|
LOOP(i) out.x[i] = 0.0;
|
|
LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, i, j) * x.x[j];
|
|
|
|
return out;
|
|
}
|
|
|
|
vector_t apply_transpose(gsl_matrix *m, vector_t x)
|
|
{
|
|
vector_t out;
|
|
|
|
LOOP(i) out.x[i] = 0.0;
|
|
LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, j, i) * x.x[j];
|
|
|
|
return out;
|
|
}
|
|
|
|
vector_t apply_inverse(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, (i+1)%3, (j+1)%3) * gsl_matrix_get(m, (i+2)%3, (j+2)%3)
|
|
- gsl_matrix_get(m, (i+1)%3, (j+2)%3) * gsl_matrix_get(m, (i+2)%3, (j+1)%3);
|
|
out.x[i] += cofactor * in.x[j];
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
|
|
{
|
|
gsl_matrix *tmp = getTempMatrix(ctx->ws);
|
|
gsl_matrix *ev = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
gsl_matrix_set_identity(tmp);
|
|
for(int i = 0; i < strlen(word); i++) {
|
|
if(word[i] == ' ')
|
|
continue;
|
|
multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
|
|
}
|
|
int count = real_eigenvectors(tmp, ev, ctx->ws);
|
|
|
|
LOOP(i) LOOP(j) out[i].x[j] = gsl_matrix_get(ev, j, i);
|
|
|
|
releaseTempMatrices(ctx->ws, 5);
|
|
|
|
return count;
|
|
}
|
|
|
|
int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
|
|
{
|
|
gsl_matrix *tmp = getTempMatrix(ctx->ws);
|
|
gsl_vector *ev = getTempVector(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
gsl_matrix_set_identity(tmp);
|
|
for(int i = 0; i < strlen(word); i++) {
|
|
if(word[i] == ' ')
|
|
continue;
|
|
multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
|
|
}
|
|
int count = real_eigenvalues(tmp, ev, ctx->ws);
|
|
|
|
LOOP(i) out[i] = gsl_vector_get(ev, i);
|
|
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
releaseTempVectors(ctx->ws, 1);
|
|
|
|
return count;
|
|
}
|
|
|
|
// level 1: the elementary drawing functions, drawPoint, drawSegment2d
|
|
|
|
void drawPoint(DrawingContext *ctx, point_t p)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_save(C);
|
|
cairo_arc(C, p.x, p.y, 3.0/ctx->dim->scalefactor, 0, 2*M_PI);
|
|
cairo_close_path(C);
|
|
cairo_fill(C);
|
|
cairo_restore(C);
|
|
|
|
/*
|
|
cairo_save(C);
|
|
cairo_move_to(C, p.x, p.y);
|
|
cairo_close_path(C);
|
|
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
|
|
cairo_set_line_width(C, 10.0/ctx->dim->scalefactor);
|
|
cairo_stroke(C);
|
|
cairo_restore(C);
|
|
*/
|
|
}
|
|
|
|
void drawSegment2d(DrawingContext *ctx, point_t a, point_t b)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
cairo_move_to(C, a.x, a.y);
|
|
cairo_line_to(C, b.x, b.y);
|
|
cairo_stroke(C);
|
|
}
|
|
|
|
// level 2: drawVector, drawCovector, drawSegment
|
|
|
|
point_t vectorToPoint(DrawingContext *ctx, vector_t in)
|
|
{
|
|
double x[3];
|
|
point_t out;
|
|
|
|
LOOP(i) x[i] = 0.0;
|
|
LOOP(i) LOOP(j) x[i] += gsl_matrix_get(ctx->cob, i, j) * in.x[j];
|
|
|
|
out.x = x[0] / x[2];
|
|
out.y = x[1] / x[2];
|
|
|
|
return out;
|
|
}
|
|
|
|
void drawVector(DrawingContext *ctx, vector_t v)
|
|
{
|
|
drawPoint(ctx, vectorToPoint(ctx, v));
|
|
}
|
|
|
|
static void drawImplicitLine(DrawingContext *ctx, double a, double b, double c)
|
|
{
|
|
double norm, lambda;
|
|
point_t m, s, xminus, xplus;
|
|
m.x = ctx->dim->center_x;
|
|
m.y = ctx->dim->center_y;
|
|
lambda = (a*m.x + b*m.y + c)/(a*a + b*b);
|
|
s.x = m.x - lambda*a;
|
|
s.y = m.y - lambda*b;
|
|
norm = sqrt(a*a + b*b);
|
|
xminus.x = s.x - ctx->dim->radius * b / norm;
|
|
xminus.y = s.y + ctx->dim->radius * a / norm;
|
|
xplus.x = s.x + ctx->dim->radius * b / norm;
|
|
xplus.y = s.y - ctx->dim->radius * a / norm;
|
|
|
|
drawSegment2d(ctx, xminus, xplus);
|
|
}
|
|
|
|
void drawCovector(DrawingContext *ctx, vector_t v)
|
|
{
|
|
double x[3];
|
|
double cofactor;
|
|
|
|
LOOP(i) x[i] = 0.0;
|
|
LOOP(i) LOOP(j) {
|
|
cofactor = gsl_matrix_get(ctx->cob, (i+1)%3, (j+1)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+2)%3)
|
|
- gsl_matrix_get(ctx->cob, (i+1)%3, (j+2)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+1)%3);
|
|
x[i] += cofactor * v.x[j];
|
|
}
|
|
|
|
drawImplicitLine(ctx, x[0], x[1], x[2]);
|
|
}
|
|
|
|
void drawSegment(DrawingContext *ctx, vector_t a, vector_t b)
|
|
{
|
|
drawSegment2d(ctx, vectorToPoint(ctx, a), vectorToPoint(ctx, b));
|
|
}
|
|
|
|
void drawSegmentWith(DrawingContext *ctx, vector_t a, vector_t b, vector_t line, int contains)
|
|
{
|
|
point_t a_ = vectorToPoint(ctx,a);
|
|
point_t b_ = vectorToPoint(ctx,b);
|
|
double x[3];
|
|
double cofactor;
|
|
double r, tline, tminus, tplus;
|
|
double coeff0, coeff1, coeff2;
|
|
point_t m, xminus, xplus;
|
|
|
|
// multiply line with inverse of cob to get it as implicit line x in chart
|
|
LOOP(i) x[i] = 0.0;
|
|
LOOP(i) LOOP(j) {
|
|
cofactor = gsl_matrix_get(ctx->cob, (i+1)%3, (j+1)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+2)%3)
|
|
- gsl_matrix_get(ctx->cob, (i+1)%3, (j+2)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+1)%3);
|
|
x[i] += cofactor * line.x[j];
|
|
}
|
|
|
|
// t = parameter on segment of intersection with line, s(t) = a + (b-a)*t
|
|
tline = -(a_.x*x[0] + a_.y*x[1] + x[2])/((b_.x - a_.x)*x[0] + (b_.y - a_.y)*x[1]);
|
|
|
|
/*
|
|
printf("tline: %f\n", tline);
|
|
|
|
point_t s;
|
|
s.x = a_.x - (b_.x-a_.x)*tline;
|
|
s.y = a_.y - (b_.y-a_.y)*tline;
|
|
drawPoint(ctx, s);
|
|
*/
|
|
|
|
if((tline < 0 || tline > 1) != contains) {
|
|
drawSegment2d(ctx, a_, b_);
|
|
} else { // need to draw complementary segment
|
|
// find t so that s(t) is at radius r from center, |s(t)-m| = r
|
|
m.x = ctx->dim->center_x;
|
|
m.y = ctx->dim->center_y;
|
|
r = ctx->dim->radius;
|
|
// equation is coeff2 t^2 + 2 coeff1 t + coeff0 = 0
|
|
coeff0 = (a_.x - m.x)*(a_.x - m.x) + (a_.y - m.y)*(a_.y - m.y) - r*r;
|
|
coeff1 = (a_.x - m.x)*(b_.x - a_.x) + (a_.y - m.y)*(b_.y - a_.y);
|
|
coeff2 = (b_.x - a_.x)*(b_.x - a_.x) + (b_.y - a_.y)*(b_.y - a_.y);
|
|
if(coeff1*coeff1 - coeff0*coeff2 <= 0)
|
|
return;
|
|
tplus = (- coeff1 + sqrt(coeff1*coeff1 - coeff0*coeff2))/coeff2;
|
|
tminus = (- coeff1 - sqrt(coeff1*coeff1 - coeff0*coeff2))/coeff2;
|
|
xplus.x = a_.x + tplus * (b_.x - a_.x);
|
|
xplus.y = a_.y + tplus * (b_.y - a_.y);
|
|
xminus.x = a_.x + tminus * (b_.x - a_.x);
|
|
xminus.y = a_.y + tminus * (b_.y - a_.y);
|
|
if(tplus > 1)
|
|
drawSegment2d(ctx, b_, xplus);
|
|
if(tminus < 0)
|
|
drawSegment2d(ctx, a_, xminus);
|
|
}
|
|
}
|
|
|
|
// level 3: boxes and polygons
|
|
|
|
void drawPolygon(DrawingContext *ctx, int segments, int sides, ...)
|
|
{
|
|
va_list args;
|
|
vector_t first, prev, current;
|
|
|
|
va_start(args, sides);
|
|
|
|
first = va_arg(args, vector_t);
|
|
current = first;
|
|
for(int i = 0; i < sides-1; i++) {
|
|
prev = current;
|
|
current = va_arg(args, vector_t);
|
|
if(segments)
|
|
drawSegment(ctx, prev, current);
|
|
else
|
|
drawCovector(ctx, cross(prev, current));
|
|
}
|
|
if(segments)
|
|
drawSegment(ctx, current, first);
|
|
else
|
|
drawCovector(ctx, cross(current, first));
|
|
|
|
va_end(args);
|
|
}
|
|
|
|
void drawTriangle(DrawingContext *ctx, const char *word)
|
|
{
|
|
vector_t p[3];
|
|
|
|
fixedPoints(ctx, word, p);
|
|
drawPolygon(ctx, 1, 3, p[0], p[1], p[2]);
|
|
}
|
|
|
|
void drawBox(DrawingContext *ctx, const char *word1, const char *word2)
|
|
{
|
|
vector_t p[2][3],i[2];
|
|
|
|
fixedPoints(ctx, word1, p[0]);
|
|
fixedPoints(ctx, word2, p[1]);
|
|
|
|
// intersect attracting line with neutral line of the other element
|
|
for(int j = 0; j < 2; j++)
|
|
i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
|
|
|
|
drawPolygon(ctx, 1, 4, p[0][0], i[0], p[1][0], i[1]);
|
|
}
|
|
|
|
void drawBoxLines(DrawingContext *ctx, const char *word1, const char *word2)
|
|
{
|
|
vector_t p[2][3],i[2];
|
|
|
|
fixedPoints(ctx, word1, p[0]);
|
|
fixedPoints(ctx, word2, p[1]);
|
|
|
|
// intersect attracting line with neutral line of the other element
|
|
for(int j = 0; j < 2; j++)
|
|
i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
|
|
|
|
drawPolygon(ctx, 0, 4, p[0][0], i[0], p[1][0], i[1]);
|
|
}
|
|
|
|
|
|
|
|
void drawBoxStd(DrawingContext *ctx, const char *word, char base)
|
|
{
|
|
char word1[100];
|
|
char word2[100];
|
|
|
|
int len = strlen(word);
|
|
if(len*2 + 4 > 100)
|
|
return;
|
|
|
|
for(int i = 0; i < len; i++) {
|
|
word1[i] = word1[2*len+2-i] = word[i];
|
|
word2[i] = word2[2*len+2-i] = word[i];
|
|
}
|
|
word1[2*len+3] = 0;
|
|
word2[2*len+3] = 0;
|
|
|
|
LOOP(i) word1[len+i] = (base-'A'+6+i+1)%3+'a';
|
|
LOOP(i) word2[len+i] = (base-'A'+6-i-1)%3+'a';
|
|
|
|
// printf("Words: %s %s\n", word1, word2);
|
|
|
|
drawBox(ctx, word1, word2);
|
|
}
|
|
|
|
void drawRotationOrbitFrame(DrawingContext *ctx, gsl_matrix *frame, vector_t start)
|
|
{
|
|
vector_t v[3], w;
|
|
point_t p;
|
|
double parameter, startangle;
|
|
int iterations = 200;
|
|
gsl_matrix *inverse = getTempMatrix(ctx->ws);
|
|
gsl_vector *start_v = getTempVector(ctx->ws);
|
|
gsl_vector *start_in_frame = getTempVector(ctx->ws);
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
// computeRotationMatrix(ctx, frame, word);
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
|
|
|
|
LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
|
|
solve(frame, start_v, start_in_frame, ctx->ws);
|
|
parameter = gsl_vector_get(start_in_frame, 2);
|
|
parameter /= sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
|
|
gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
|
|
startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));
|
|
|
|
int previous_inside = 0;
|
|
for(int k = 0; k <= iterations; k++) {
|
|
LOOP(i) w.x[i] = parameter * v[2].x[i] + cos(2*k*M_PI/iterations) * v[0].x[i] + sin(2*k*M_PI/iterations) * v[1].x[i];
|
|
p = vectorToPoint(ctx, w);
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
|
|
cairo_stroke(C);
|
|
|
|
releaseTempMatrices(ctx->ws, 1);
|
|
releaseTempVectors(ctx->ws, 2);
|
|
}
|
|
|
|
void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
|
|
{
|
|
gsl_matrix *frame = getTempMatrix(ctx->ws);
|
|
|
|
computeRotationMatrix(ctx, frame, word);
|
|
drawRotationOrbitFrame(ctx, frame, start);
|
|
|
|
releaseTempMatrices(ctx->ws, 1);
|
|
}
|
|
|
|
void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
|
|
{
|
|
vector_t v[3], w;
|
|
point_t p;
|
|
double parameter, startangle;
|
|
int iterations = 200;
|
|
gsl_matrix *frame = getTempMatrix(ctx->ws);
|
|
gsl_matrix *inverse = getTempMatrix(ctx->ws);
|
|
gsl_vector *start_v = getTempVector(ctx->ws);
|
|
gsl_vector *start_in_frame = getTempVector(ctx->ws);
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
computeRotationMatrix(ctx, frame, word);
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
|
|
|
|
LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
|
|
// solve(frame, start_v, start_in_frame, ctx->ws);
|
|
gsl_blas_dgemv(CblasTrans, 1.0, frame, start_v, 0.0, start_in_frame);
|
|
parameter = sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
|
|
gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
|
|
parameter /= gsl_vector_get(start_in_frame, 2);
|
|
startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));
|
|
|
|
int previous_inside = 0;
|
|
for(int k = 0; k <= iterations; k++) {
|
|
LOOP(i) w.x[i] = parameter * v[2].x[i] + cos(2*k*M_PI/iterations) * v[0].x[i] + sin(2*k*M_PI/iterations) * v[1].x[i];
|
|
p = vectorToPoint(ctx, w);
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
|
|
cairo_stroke(C);
|
|
|
|
releaseTempMatrices(ctx->ws, 2);
|
|
releaseTempVectors(ctx->ws, 2);
|
|
}
|
|
|
|
void drawArcWithOutput(DrawingContext *ctx, const char *word, vector_t start, vector_type_t starttype, vector_t end, vector_type_t endtype, vector_t third, int contain, vector_t *start_vector_out, vector_t *end_vector_out, int dontdraw)
|
|
{
|
|
vector_t v[3], w, w_;
|
|
point_t p, p_;
|
|
double radius, angle_start, angle_end, angle_third, angle, angle_end_delta, sign, angle_start_final, angle_end_final, angle_end_other;
|
|
int iterations = 200;
|
|
gsl_matrix *frame = getTempMatrix(ctx->ws);
|
|
gsl_matrix *inverse = getTempMatrix(ctx->ws);
|
|
gsl_vector *vector = getTempVector(ctx->ws);
|
|
gsl_vector *vector_in_frame = getTempVector(ctx->ws);
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
computeRotationMatrix(ctx, frame, word);
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
|
|
|
|
LOOP(i) gsl_vector_set(vector, i, start.x[i]);
|
|
if(starttype == VT_POINT) {
|
|
solve(frame, vector, vector_in_frame, ctx->ws);
|
|
radius = sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
|
|
gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));
|
|
radius /= fabs(gsl_vector_get(vector_in_frame, 2));
|
|
angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
|
|
gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
|
|
} else {
|
|
gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);
|
|
radius = fabs(gsl_vector_get(vector_in_frame, 2));
|
|
radius /= sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
|
|
gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));
|
|
|
|
angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
|
|
gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
|
|
}
|
|
|
|
LOOP(i) gsl_vector_set(vector, i, third.x[i]);
|
|
solve(frame, vector, vector_in_frame, ctx->ws);
|
|
angle_third = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
|
|
gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
|
|
|
|
LOOP(i) gsl_vector_set(vector, i, end.x[i]);
|
|
if(endtype == VT_POINT) {
|
|
solve(frame, vector, vector_in_frame, ctx->ws);
|
|
angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
|
|
gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
|
|
} else {
|
|
gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);
|
|
|
|
// this is only the average angle
|
|
angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
|
|
gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
|
|
|
|
angle_end_delta = acos(-fabs(gsl_vector_get(vector_in_frame, 2))/radius/
|
|
sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
|
|
gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1)));
|
|
}
|
|
|
|
int previous_inside = 0;
|
|
|
|
for(int i = 0; i < 4; i++) {
|
|
angle_start_final = angle_start;
|
|
|
|
if(endtype == VT_POINT) {
|
|
angle_end_final = angle_end;
|
|
} else {
|
|
if(i >= 2) {
|
|
angle_end_final = angle_end - angle_end_delta;
|
|
angle_end_other = angle_end + angle_end_delta;
|
|
} else {
|
|
angle_end_final = angle_end + angle_end_delta;
|
|
angle_end_other = angle_end - angle_end_delta;
|
|
}
|
|
}
|
|
|
|
if(i%2)
|
|
FLIP(angle_start_final, angle_end_final);
|
|
|
|
if(endtype == VT_LINE && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_end_other))
|
|
continue;
|
|
if(contain && !ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
|
|
continue;
|
|
if(!contain && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
|
|
continue;
|
|
|
|
break;
|
|
}
|
|
|
|
// output the start end end point
|
|
/*
|
|
LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle_start_final) * v[0].x[i] + sin(angle_start_final) * v[1].x[i];
|
|
p = vectorToPoint(ctx, w);
|
|
LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle_end_final) * v[0].x[i] + sin(angle_end_final) * v[1].x[i];
|
|
p_ = vectorToPoint(ctx, w);
|
|
printf("\\draw (%f,%f) -- (%f,%f);\n", p.x, p.y, p_.x, p_.y);
|
|
*/
|
|
|
|
if(!dontdraw) {
|
|
for(int k = 0; k <= iterations; k++) {
|
|
angle = angle_start_final + (double)k/(double)iterations * ANGLE_DIFF(angle_end_final, angle_start_final);
|
|
|
|
LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle) * v[0].x[i] + sin(angle) * v[1].x[i];
|
|
p = vectorToPoint(ctx, w);
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
if(start_vector_out)
|
|
LOOP(i) start_vector_out->x[i] = v[2].x[i] / radius +
|
|
cos(angle_start_final) * v[0].x[i] +
|
|
sin(angle_start_final) * v[1].x[i];
|
|
if(end_vector_out)
|
|
LOOP(i) end_vector_out->x[i] = v[2].x[i] / radius +
|
|
cos(angle_end_final) * v[0].x[i] +
|
|
sin(angle_end_final) * v[1].x[i];
|
|
|
|
cairo_stroke(C);
|
|
|
|
releaseTempMatrices(ctx->ws, 2);
|
|
releaseTempVectors(ctx->ws, 2);
|
|
}
|
|
|
|
void drawArc(DrawingContext *ctx, const char *word, vector_t start, vector_type_t starttype, vector_t end, vector_type_t endtype, vector_t third, int contain)
|
|
{
|
|
drawArcWithOutput(ctx, word, start, starttype, end, endtype, third, contain, 0, 0, 0);
|
|
}
|
|
|
|
// level 4: draw the actual image components
|
|
|
|
void drawReflectors(DrawingContext *ctx)
|
|
{
|
|
vector_t v[3];
|
|
|
|
cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
|
|
|
|
LOOP(i) LOOP(j) { v[i].x[j] = (i==j) ? 1.0 : 0.0; }
|
|
LOOP(i) drawVector(ctx, v[i]);
|
|
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
|
|
LOOP(i) drawCovector(ctx, v[i]);
|
|
}
|
|
|
|
void drawAttractors(DrawingContext *ctx)
|
|
{
|
|
int n = 3;
|
|
vector_t p[6][3];
|
|
vector_t l[6][3];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
fixedPoints(ctx, "a cab a", p[3]);
|
|
fixedPoints(ctx, "b abc b", p[4]);
|
|
fixedPoints(ctx, "c bca c", p[5]);
|
|
|
|
double color[6][3] = {{1,0,0},{0,0.7,0},{0,0,1},{0,1,1},{0,1,1},{0,1,1}};
|
|
|
|
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) {
|
|
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
|
|
drawVector(ctx, p[i][j]);
|
|
}
|
|
|
|
for(int i = 0; i < n; i++) LOOP(j) {
|
|
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
|
|
drawCovector(ctx, l[i][j]);
|
|
}
|
|
}
|
|
|
|
char *conjugate_word(const char *word, int modifier, const char *conj, char *buffer)
|
|
{
|
|
int wordlen = strlen(word);
|
|
int conjlen = strlen(conj);
|
|
|
|
for(int i = 0; i < conjlen; i++) {
|
|
buffer[i] = conj[i];
|
|
buffer[2*conjlen+wordlen-1-i] = conj[i];
|
|
}
|
|
|
|
for(int i = 0; i < wordlen; i++) {
|
|
if(word[i] == ' ')
|
|
buffer[conjlen+i] = word[i];
|
|
else
|
|
buffer[conjlen+i] = (word[i]+modifier-'a')%3 + 'a';
|
|
}
|
|
|
|
buffer[2*conjlen + wordlen] = 0;
|
|
|
|
return buffer;
|
|
}
|
|
|
|
void drawCurvedBox(DrawingContext *ctx, int base, const char *conj, int style)
|
|
{
|
|
vector_t p[11][3];
|
|
vector_t l[2][3];
|
|
vector_t corner1, corner2;
|
|
vector_t tmp1, tmp2;
|
|
char word[100];
|
|
int modifier = base - 'A';
|
|
|
|
conjugate_word("abc", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[0]);
|
|
conjugate_word("bca", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[1]);
|
|
conjugate_word("b abc b", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[2]);
|
|
conjugate_word("ab abc ba", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[3]);
|
|
conjugate_word("baca cab acab", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[4]);
|
|
conjugate_word("abaca cab acaba", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[5]);
|
|
conjugate_word("bca cab acb", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[6]);
|
|
conjugate_word("abca cab acba", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[7]);
|
|
conjugate_word("abacababa", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[8]);
|
|
conjugate_word("bacabab", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[9]);
|
|
conjugate_word("cab", modifier, conj, word);
|
|
fixedPoints(ctx, word, p[10]);
|
|
|
|
|
|
// conjugate_word("bca b abc b acb", modifier, conj, word);
|
|
// fixedPoints(ctx, word, p[6]);
|
|
// conjugate_word("bca baca cab acab acb", modifier, conj, word);
|
|
// fixedPoints(ctx, word, p[7]);
|
|
|
|
|
|
LOOP(j) l[0][j] = cross(p[0][(3-j)%3], p[0][(4-j)%3]);
|
|
LOOP(j) l[1][j] = cross(p[1][(3-j)%3], p[1][(4-j)%3]);
|
|
LOOP(j) l[10][j] = cross(p[10][(3-j)%3], p[10][(4-j)%3]);
|
|
|
|
// main conic
|
|
conjugate_word("ab", modifier, conj, word);
|
|
drawArcWithOutput(ctx, word, p[0][0], VT_POINT, p[2][0], VT_POINT, p[1][0], 0, &tmp1, &tmp2, style != 1);
|
|
if(style == 2)
|
|
drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
|
|
if(style == 3) {
|
|
drawVector(ctx, tmp1);
|
|
drawVector(ctx, tmp2);
|
|
}
|
|
|
|
conjugate_word("ab", modifier, conj, word);
|
|
drawArcWithOutput(ctx, word, p[1][0], VT_POINT, p[3][0], VT_POINT, p[0][0], 0, &tmp1, &tmp2, style != 1);
|
|
if(style == 2)
|
|
drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
|
|
if(style == 3) {
|
|
drawVector(ctx, tmp1);
|
|
drawVector(ctx, tmp2);
|
|
}
|
|
|
|
conjugate_word("bcabcb", modifier, conj, word);
|
|
drawArcWithOutput(ctx, word, p[2][0], VT_POINT, l[1][0], VT_LINE, p[6][0], 1, &tmp1, &tmp2, style != 1); // only 1st cutoff
|
|
if(style == 2)
|
|
drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
|
|
|
|
corner1 = tmp2;
|
|
|
|
conjugate_word("abcabcba", modifier, conj, word);
|
|
drawArcWithOutput(ctx, word, p[3][0], VT_POINT, l[0][0], VT_LINE, p[7][0], 1, &tmp1, &tmp2, style != 1); // only 1st cutoff
|
|
if(style == 2)
|
|
drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
|
|
corner2 = tmp2;
|
|
|
|
if(style == 1 || style == 2) {
|
|
drawSegmentWith(ctx, p[0][0], corner2, l[1][1], 0);
|
|
drawSegmentWith(ctx, p[1][0], corner1, l[0][1], 0);
|
|
} else if(style == 3)
|
|
{
|
|
drawVector(ctx, corner1);
|
|
drawVector(ctx, corner2);
|
|
}
|
|
}
|
|
|
|
|
|
void drawBoxes(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
gsl_matrix *frame = getTempMatrix(ctx->ws);
|
|
cairo_t *C = ctx->cairo;
|
|
cairo_save(C);
|
|
|
|
vector_t p[22][3];
|
|
vector_t l[22][3];
|
|
vector_t alpha[6];
|
|
vector_t ptmp[3];
|
|
char word[100], word2[100];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
fixedPoints(ctx, "bacabab", p[3]);
|
|
fixedPoints(ctx, "bcacabacb", p[4]);
|
|
|
|
cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
|
|
cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
|
|
|
|
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, "ca", p[0][0]);
|
|
|
|
/*
|
|
for(int i = 0; i < 18; i++) {
|
|
if(i == 0)
|
|
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]));
|
|
|
|
// drawRotationOrbit(ctx, "abca", p[0][0]);
|
|
|
|
cairo_restore(C);
|
|
releaseTempMatrices(ctx->ws, 5);
|
|
}
|
|
|
|
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)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
gsl_vector *marking_globalbasis = getTempVector(ctx->ws);
|
|
gsl_vector *marking_drawbasis = getTempVector(ctx->ws);
|
|
cairo_t *C = ctx->cairo;
|
|
cairo_save(C);
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
vector_t p[4][3];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
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];
|
|
LOOP(i) vertex[i] = cross(
|
|
cross(p[(i+1)%3][0],p[(i+1)%3][2]),
|
|
cross(p[(i+2)%3][0],p[(i+2)%3][2]));
|
|
|
|
LOOP(i) drawVector(ctx, vertex[i]);
|
|
// LOOP(i) drawCovector(ctx, att_line[i]);
|
|
|
|
double half_cross_ratio[3];
|
|
LOOP(i) half_cross_ratio[i] = scal(vertex[(i+1)%3],att_line[i])/scal(vertex[(i+2)%3],att_line[i]);
|
|
double triple_ratio = half_cross_ratio[0]*half_cross_ratio[1]*half_cross_ratio[2];
|
|
LOOP(i) half_cross_ratio[i] = scal(vertex[(i+1)%3],rep_line[i])/scal(vertex[(i+2)%3],rep_line[i]);
|
|
double triple_ratio2 = half_cross_ratio[0]*half_cross_ratio[1]*half_cross_ratio[2];
|
|
|
|
|
|
|
|
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,
|
|
marking, marking2, 1, &boundary_point[0], &value[0]);
|
|
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
|
|
marking2, marking3, 1, &boundary_point[1], &value[1]);
|
|
getMinMaxHalfCrossRatio(ctx->limit_curve, ctx->n_group_elements,
|
|
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;
|
|
LOOP(j) LOOP(k) fp[j].x[k] = ctx->limit_curve[12*boundary_point[0]+3+3*j+k];
|
|
tangent = cross(fp[0],fp[1]);
|
|
drawCovector(ctx, tangent);*/
|
|
|
|
snprintf(ctx->extra_text, 1000, "tr1 = %f, tr2 2 = %f, aa = %f",
|
|
log(value[0])+log(value[1])+log(value[2]),
|
|
-log(value[3])-log(value[4])-log(value[5]),
|
|
log(value[0])+log(value[1])+log(value[2])+log(value[3])+log(value[4])+log(value[5]));
|
|
|
|
drawCovector(ctx, cross(marking, marking2));
|
|
drawCovector(ctx, cross(marking2, marking3));
|
|
drawCovector(ctx, cross(marking3, marking));
|
|
|
|
cairo_restore(C);
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
releaseTempVectors(ctx->ws, 2);
|
|
}
|
|
|
|
void drawRotatedReflectors(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
cairo_t *C = ctx->cairo;
|
|
vector_t fp[3], fp2[3];
|
|
vector_t w;
|
|
vector_t v[3];
|
|
|
|
cairo_set_source_rgb(C, 0.7, 0.7, 0.7);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
|
|
multiply(gen[0], gen[1], rot);
|
|
|
|
for(int j = 0; j < ctx->p[2]; j++) {
|
|
drawCovector(ctx, v[0]);
|
|
v[0] = apply_transpose(rot, v[0]);
|
|
}
|
|
|
|
LOOP(i) LOOP(j) { v[i].x[j] = (i==j) ? 1.0 : 0.0; }
|
|
|
|
for(int j = 0; j < ctx->p[2]; j++) {
|
|
drawVector(ctx, v[0]);
|
|
v[0] = apply(rot, v[0]);
|
|
}
|
|
|
|
fixedPoints(ctx, "cab", fp);
|
|
fixedPoints(ctx, "cacabac", fp2);
|
|
drawRotationOrbit(ctx, "ac", fp[0]);
|
|
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
}
|
|
|
|
void drawDualLimitCurve(DrawingContext *ctx)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_save(C);
|
|
cairo_set_source_rgb(C, 0.5, 0.5, 1);
|
|
|
|
int n = 18;
|
|
vector_t p[n][3];
|
|
vector_t l[n][3];
|
|
vector_t ptmp[3], ltmp[3];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "ab abc ba", p[1]);
|
|
fixedPoints(ctx, "abab abc baba", p[2]);
|
|
fixedPoints(ctx, "ababab abc bababa", p[3]);
|
|
fixedPoints(ctx, "abababab abc babababa", p[4]);
|
|
fixedPoints(ctx, "babababa abc abababab", p[5]);
|
|
fixedPoints(ctx, "bababa abc ababab", p[6]);
|
|
fixedPoints(ctx, "baba abc abab", p[7]);
|
|
fixedPoints(ctx, "ba abc ab", p[8]);
|
|
|
|
fixedPoints(ctx, "bca", p[9]);
|
|
fixedPoints(ctx, "ab bca ba", p[10]);
|
|
fixedPoints(ctx, "abab bca baba", p[11]);
|
|
fixedPoints(ctx, "ababab bca bababa", p[12]);
|
|
fixedPoints(ctx, "abababab bca babababa", p[13]);
|
|
fixedPoints(ctx, "babababa bca abababab", p[14]);
|
|
fixedPoints(ctx, "bababa bca ababab", p[15]);
|
|
fixedPoints(ctx, "baba bca abab", p[16]);
|
|
fixedPoints(ctx, "ba bca ab", p[17]);
|
|
|
|
/*
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "ac abc ca", p[1]);
|
|
fixedPoints(ctx, "acac abc caca", p[2]);
|
|
fixedPoints(ctx, "acacac abc cacaca", p[3]);
|
|
fixedPoints(ctx, "acacacac abc cacacaca", p[4]);
|
|
fixedPoints(ctx, "cacacaca abc acacacac", p[5]);
|
|
fixedPoints(ctx, "cacaca abc acacac", p[6]);
|
|
fixedPoints(ctx, "caca abc acac", p[7]);
|
|
fixedPoints(ctx, "ca abc ac", p[8]);
|
|
|
|
fixedPoints(ctx, "bca", p[9]);
|
|
fixedPoints(ctx, "ac bca ca", p[10]);
|
|
fixedPoints(ctx, "acac bca caca", p[11]);
|
|
fixedPoints(ctx, "acacac bca cacaca", p[12]);
|
|
fixedPoints(ctx, "acacacac bca cacacaca", p[13]);
|
|
fixedPoints(ctx, "cacacaca bca acacacac", p[14]);
|
|
fixedPoints(ctx, "cacaca bca acacac", p[15]);
|
|
fixedPoints(ctx, "caca bca acac", p[16]);
|
|
fixedPoints(ctx, "ca bca ac", p[17]);
|
|
*/
|
|
|
|
/*
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
fixedPoints(ctx, "b abc b", p[3]);
|
|
fixedPoints(ctx, "c bca c", p[4]);
|
|
fixedPoints(ctx, "a cab a", p[5]);
|
|
*/
|
|
|
|
/*
|
|
for(int i = 0; i < n; i++) {
|
|
LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
|
|
drawCovector(ctx, l[i][0]);
|
|
// drawCovector(ctx, l[i][2]);
|
|
}*/
|
|
|
|
fixedPoints(ctx, "abc", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
fixedPoints(ctx, "bca", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
fixedPoints(ctx, "cab", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
fixedPoints(ctx, "babcb", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
fixedPoints(ctx, "cbcac", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
fixedPoints(ctx, "acaba", ptmp);
|
|
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
|
|
|
|
cairo_restore(C);
|
|
}
|
|
|
|
void drawLimitCurve(DrawingContext *ctx)
|
|
{
|
|
int close_points = 0;
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_save(C);
|
|
|
|
// cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
|
|
cairo_set_source_rgb(C, 0, 0, 0);
|
|
|
|
if(ctx->limit_with_lines) {
|
|
int previous_inside = 0;
|
|
cairo_new_path(C);
|
|
|
|
for(int i = 0; i < ctx->limit_curve_count; i++) {
|
|
point_t p;
|
|
p.x = ctx->limit_curve[12*i];
|
|
p.y = ctx->limit_curve[12*i+1];
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
|
|
cairo_stroke(C);
|
|
} else {
|
|
for(int i = 0; i < ctx->limit_curve_count; i++) {
|
|
point_t p;
|
|
p.x = ctx->limit_curve[12*i];
|
|
p.y = ctx->limit_curve[12*i+1];
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
cairo_arc(C, p.x, p.y, 2.0/ctx->dim->scalefactor, 0, 2*M_PI);
|
|
cairo_close_path(C);
|
|
cairo_fill(C);
|
|
}
|
|
}
|
|
}
|
|
|
|
cairo_restore(C);
|
|
}
|
|
|
|
void drawCoxeterOrbit(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
gsl_vector *eval = getTempVector(ctx->ws);
|
|
gsl_matrix *coxeter_fixedpoints = getTempMatrix(ctx->ws);
|
|
gsl_vector *startpoint_coxeterbasis = getTempVector(ctx->ws);
|
|
gsl_vector *startpoint_globalbasis = getTempVector(ctx->ws);
|
|
gsl_vector *startpoint_drawbasis = getTempVector(ctx->ws);
|
|
gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);
|
|
|
|
cairo_t *C = ctx->cairo;
|
|
vector_t cox[3][3];
|
|
vector_t abcb[3];
|
|
double ev[3];
|
|
vector_t v, start;
|
|
point_t p;
|
|
int first = 1;
|
|
|
|
cairo_save(C);
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
cairo_set_source_rgb(C, 0, 0, 1);
|
|
|
|
fixedPoints(ctx, "abc", cox[0]);
|
|
fixedPoints(ctx, "bca", cox[1]);
|
|
fixedPoints(ctx, "cab", cox[2]);
|
|
// fixedPoints(ctx, "babc", abcb);
|
|
wordEigenvalues(ctx, "abc", ev);
|
|
LOOP(i) LOOP(j) gsl_matrix_set(coxeter_fixedpoints, j, i, cox[0][i].x[j]);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
gsl_matrix_set_identity(elements[0]);
|
|
for(int i = 1; i < ctx->n_group_elements; i++)
|
|
multiply(gen[ctx->group[i].letter], elements[ctx->group[i].parent->id], elements[i]);
|
|
|
|
//printf("coxeter eigenvalues: %f %f %f\n", ev[0], ev[1], ev[2]);
|
|
|
|
// LOOP(i) gsl_vector_set(startpoint_globalbasis, i, cox[1][0].x[i]);
|
|
|
|
gsl_vector_set(startpoint_drawbasis, 0, ctx->marking.x);
|
|
gsl_vector_set(startpoint_drawbasis, 1, ctx->marking.y);
|
|
gsl_vector_set(startpoint_drawbasis, 2, 1);
|
|
solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);
|
|
|
|
solve(coxeter_fixedpoints, startpoint_globalbasis, startpoint_coxeterbasis, ctx->ws);
|
|
// LOOP(i) start.x[i] = gsl_vector_get(startpoint_coxeterbasis, i);
|
|
|
|
LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);
|
|
|
|
/*
|
|
for(int t = -1000; t < 1000; t++) {
|
|
LOOP(i) v.x[i] = 0;
|
|
LOOP(i) LOOP(j) v.x[j] += pow(fabs(ev[i]),t*0.01)*start.x[i]*cox[0][i].x[j];
|
|
p = vectorToPoint(ctx, v);
|
|
|
|
if(first) {
|
|
cairo_move_to(C, p.x, p.y);
|
|
first = 0;
|
|
} else {
|
|
cairo_line_to(C, p.x, p.y);
|
|
}
|
|
}
|
|
cairo_stroke(C);
|
|
*/
|
|
|
|
for(int i = 0; i < ctx->n_group_elements; i++) {
|
|
v = apply(elements[i], start);
|
|
drawVector(ctx, v);
|
|
// ctx->limit_curve[3*i+2] = atan2(
|
|
// gsl_matrix_get(fixedpoints_pos, 2, column)/gsl_matrix_get(fixedpoints_pos, 0, column),
|
|
// gsl_matrix_get(fixedpoints_pos, 1, column)/gsl_matrix_get(fixedpoints_pos, 0, column));
|
|
}
|
|
|
|
|
|
/* for(int t = -20; t < 20; t++) {
|
|
LOOP(i) v.x[i] = 0;
|
|
LOOP(i) LOOP(j) v.x[j] += (ev[i]<0&&t%2?-1:1)*pow(fabs(ev[i]),t/3.0)*start.x[i]*cox[0][i].x[j];
|
|
drawVector(ctx, v);
|
|
}*/
|
|
|
|
cairo_set_source_rgb(C, 0, 0, 0);
|
|
// LOOP(i) drawVector(ctx, abcb[i]);
|
|
|
|
cairo_restore(C);
|
|
releaseTempMatrices(ctx->ws, 5 + ctx->n_group_elements);
|
|
releaseTempVectors(ctx->ws, 4);
|
|
}
|
|
|
|
void drawText(DrawingContext *ctx)
|
|
{
|
|
cairo_move_to(ctx->cairo, 15, 30);
|
|
cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
|
|
char buf[1000];
|
|
snprintf(buf, 1000, "t = exp(%.8f) = %.8f, %s", log(ctx->parameter), ctx->parameter, ctx->extra_text);
|
|
cairo_show_text(ctx->cairo, buf);
|
|
}
|
|
|
|
// level 5: put everything together
|
|
|
|
void draw(DrawingContext *ctx)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_set_source_rgb(C, 1, 1, 1);
|
|
cairo_paint(C);
|
|
|
|
cairo_set_matrix(C, &ctx->dim->matrix);
|
|
|
|
// defaults; use save/restore whenever these are changed
|
|
cairo_set_line_width(C, 1.0/ctx->dim->scalefactor);
|
|
cairo_set_font_size(C, 16);
|
|
cairo_set_line_join(C, CAIRO_LINE_JOIN_BEVEL);
|
|
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
|
|
|
|
if(ctx->limit_curve_count >= 0) {
|
|
if(ctx->show_limit)
|
|
drawLimitCurve(ctx);
|
|
|
|
if(ctx->show_dual_limit)
|
|
drawDualLimitCurve(ctx);
|
|
|
|
if(ctx->show_attractors)
|
|
drawAttractors(ctx);
|
|
|
|
if(ctx->show_rotated_reflectors)
|
|
drawRotatedReflectors(ctx);
|
|
|
|
if(ctx->show_reflectors)
|
|
drawReflectors(ctx);
|
|
|
|
if(ctx->show_boxes)
|
|
drawBoxes(ctx);
|
|
|
|
if(ctx->show_boxes2)
|
|
drawBoxes2(ctx);
|
|
|
|
if(ctx->show_marking)
|
|
{
|
|
cairo_set_source_rgb(C, 0, 0, 1);
|
|
drawPoint(ctx, ctx->marking);
|
|
drawPoint(ctx, ctx->marking2);
|
|
drawPoint(ctx, ctx->marking3);
|
|
}
|
|
|
|
if(ctx->show_coxeter_orbit)
|
|
drawCoxeterOrbit(ctx);
|
|
}
|
|
|
|
cairo_identity_matrix(C); // text is in screen coordinates
|
|
|
|
if(ctx->show_text)
|
|
drawText(ctx);
|
|
|
|
cairo_surface_flush(cairo_get_target(C));
|
|
}
|