void PathRenderer::subdivide_bezier(int level, float cp0_x, float cp0_y, float cp1_x, float cp1_y, float cp2_x, float cp2_y, float cp3_x, float cp3_y, float t0, float t1)
{
const float split_angle_cos = 0.99f;
float tc = (t0 + t1) * 0.5f;
clan::Pointf sp = point_on_bezier(cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, t0);
clan::Pointf cp = point_on_bezier(cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, tc);
clan::Pointf ep = point_on_bezier(cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, t1);
clan::Vec2f sp2cp(cp.x - sp.x, cp.y - sp.y);
clan::Vec2f cp2ep(ep.x - cp.x, ep.y - cp.y);
float dot = clan::Vec2f::dot(sp2cp.normalize(), cp2ep.normalize());
if (dot < split_angle_cos && level < 15)
{
subdivide_bezier(level + 1, cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, t0, tc);
subdivide_bezier(level + 1, cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, tc, t1);
}
else
{
line(ep.x, ep.y);
}
}
void PathRenderer::cubic_bezier(float cp1_x, float cp1_y, float cp2_x, float cp2_y, float cp3_x, float cp3_y)
{
float cp0_x = last_x;
float cp0_y = last_y;
float estimated_length =
std::sqrt((cp1_x - cp0_x) * (cp1_x - cp0_x) + (cp1_y - cp0_y) * (cp1_y - cp0_y)) +
std::sqrt((cp1_x - cp0_x) * (cp1_x - cp0_x) + (cp1_y - cp0_y) * (cp1_y - cp0_y)) +
std::sqrt((cp1_x - cp0_x) * (cp1_x - cp0_x) + (cp1_y - cp0_y) * (cp1_y - cp0_y));
float min_segs = 10.0f;
float segs = estimated_length / 5.0f;
int steps = (int)std::ceil(std::sqrt(segs * segs * 0.3f + min_segs));
for (int i = 0; i < steps; i++)
{
//clan::Pointf sp = point_on_bezier(cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, i / (float)steps);
clan::Pointf ep = point_on_bezier(cp0_x, cp0_y, cp1_x, cp1_y, cp2_x, cp2_y, cp3_x, cp3_y, (i + 1) / (float)steps);
line(ep.x, ep.y);
}
// http://ciechanowski.me/blog/2014/02/18/drawing-bezier-curves/
// http://antigrain.com/research/adaptive_bezier/ (best method, unfortunately GPL example code)
}
//returns the distance along the edge which is farthest from the other edges
double fatgraph_remotest(fatgraph* fg, int edge) {
//go through 100 points on edge and find the one which is farthest from
//all the other edges
vector2d currentPoint;
double currentDist;
double minDistToThisPoint;
double pointMaxDistAway;
double maxDist;
double i;
int j;
int k;
vector2d* bezier1 = (vector2d*)malloc((fg->num_edges)*sizeof(vector2d));
vector2d* bezier2 = (vector2d*)malloc((fg->num_edges)*sizeof(vector2d));
for (j=0; j<fg->num_edges; j++) {
//find the beziers
for (k=0; k<fg->verts[fg->edges[j].start].num_edges; k++) {
if (j == fg->verts[fg->edges[j].start].edges[k]
&& fg->verts[fg->edges[j].start].edges_initial[k] == 1) {
bezier1[j] = fg->verts[fg->edges[j].start].bezier[k];
break;
}
}
for (k=0; k<fg->verts[fg->edges[j].end].num_edges; k++) {
if (j == fg->verts[fg->edges[j].end].edges[k]
&& fg->verts[fg->edges[j].end].edges_initial[k] == 0) {
bezier2[j] = fg->verts[fg->edges[j].end].bezier[k];
break;
}
}
bezier1[j] = vector2d_add(fg->verts[fg->edges[j].start].loc, bezier1[j]);
bezier2[j] = vector2d_add(fg->verts[fg->edges[j].end].loc, bezier2[j]);
}
//printf("I'm finding the remotest point on edge %d\n", edge);
//now find the best point
maxDist = 0;
for (i=0; i<1; i+=0.01) {
minDistToThisPoint = 1e8;
currentPoint = point_on_bezier(fg->verts[fg->edges[edge].start].loc,
fg->verts[fg->edges[edge].end].loc,
bezier1[edge],
bezier2[edge],
i);
//distances to edges
for (j=0; j<fg->num_edges; j++) {
if (j==edge) {
continue;
}
currentDist = distance_to_bezier_fast(fg->verts[fg->edges[j].start].loc,
fg->verts[fg->edges[j].end].loc,
bezier1[j],
bezier2[j],
currentPoint.x,
currentPoint.y);
if (currentDist < minDistToThisPoint) {
minDistToThisPoint = currentDist;
}
}
//distances to vertices
for (j=0; j<fg->num_verts; j++) {
currentDist = sqrt( (currentPoint.x - fg->verts[j].loc.x)*
(currentPoint.x - fg->verts[j].loc.x) +
(currentPoint.y - fg->verts[j].loc.y)*
(currentPoint.y - fg->verts[j].loc.y) );
if (currentDist < minDistToThisPoint) {
minDistToThisPoint = currentDist;
}
}
if (minDistToThisPoint > maxDist) {
maxDist = minDistToThisPoint;
pointMaxDistAway = i;
//printf("New remotest point (distance %f) at %f\n", maxDist, i);
}
}
free(bezier1);
free(bezier2);
return pointMaxDistAway;
}