summaryrefslogtreecommitdiff
path: root/bezier.cpp
diff options
context:
space:
mode:
Diffstat (limited to 'bezier.cpp')
-rw-r--r--bezier.cpp157
1 files changed, 157 insertions, 0 deletions
diff --git a/bezier.cpp b/bezier.cpp
new file mode 100644
index 0000000..4e0cb5c
--- /dev/null
+++ b/bezier.cpp
@@ -0,0 +1,157 @@
+// A modified version of the bezier code in ImGui with extra features for bitmap and path interaction.
+
+// Function to convert a ratio back into a point for the bezier handles.
+v2 Line_RatioToPoint(v2 a, v2 b, real32 ratio)
+{
+ v2 ab_dir = b - a;
+ real32 ab_len_sqr = ab_dir.x * ab_dir.x + ab_dir.y * ab_dir.y;
+ real32 dot = ratio*ab_len_sqr;
+ return a + ab_dir * dot / V2(ab_len_sqr);
+}
+
+// The ratio here is just the dot product divided by the squared length.
+v2 Bezier_LineClosestPoint2(v2 a, v2 b, v2 p, real32 *ratio)
+{
+ v2 ap = p - a;
+ v2 ab_dir = b - a;
+ real32 dot = ap.x * ab_dir.x + ap.y * ab_dir.y;
+ if (dot < 0.0f) {
+ *ratio = 0.0f;
+ return a;
+ }
+ real32 ab_len_sqr = ab_dir.x * ab_dir.x + ab_dir.y * ab_dir.y;
+ if (dot > ab_len_sqr) {
+ *ratio = 1.0f;
+ return b;
+ }
+ *ratio = dot / ab_len_sqr;
+ return a + ab_dir * dot / ab_len_sqr;
+}
+
+// Following the algorithm, we take the ratio from the _leftmost_ point in each
+// subdivision of the cubic spline until we're within tess_tol, and then we
+// interpolate it with the subdivision's rightmost point in the ClosestPoint call.
+// The pow(0.5, level) represents the ratio of the next subdivision's leftmost
+// point (AKA the rightmost point of the current subdivision).
+
+// finds the point closest to p and also fills out its ratio along the curve
+static void Bezier_CubicClosestPointCasteljauStep(v2 p, v2 *p_closest, real32 ratio, real32 *r_closest, v2 *p_last, real32 *p_closest_dist2,
+ real32 x1, real32 y1, real32 x2, real32 y2, real32 x3, real32 y3, real32 x4, real32 y4, real32 tess_tol, int level)
+{
+ real32 dx = x4 - x1;
+ real32 dy = y4 - y1;
+ real32 d2 = ((x2 - x4) * dy - (y2 - y4) * dx);
+ real32 d3 = ((x3 - x4) * dy - (y3 - y4) * dx);
+ d2 = (d2 >= 0) ? d2 : -d2;
+ d3 = (d3 >= 0) ? d3 : -d3;
+ if ((d2 + d3) * (d2 + d3) < tess_tol * (dx * dx + dy * dy))
+ {
+ v2 p_current = V2(x4, y4);
+ real32 added_ratio;
+ v2 p_line = Bezier_LineClosestPoint2(*p_last, p_current, p, &added_ratio);
+ real32 dist2 = LengthSq(p - p_line);
+ if (dist2 < *p_closest_dist2)
+ {
+ *p_closest = p_line;
+ *p_closest_dist2 = dist2;
+ *r_closest = ratio + pow(0.5, level)*added_ratio;
+ }
+ *p_last = p_current;
+ }
+ else if (level < 10)
+ {
+ real32 x12 = (x1 + x2)*0.5f, y12 = (y1 + y2)*0.5f;
+ real32 x23 = (x2 + x3)*0.5f, y23 = (y2 + y3)*0.5f;
+ real32 x34 = (x3 + x4)*0.5f, y34 = (y3 + y4)*0.5f;
+ real32 x123 = (x12 + x23)*0.5f, y123 = (y12 + y23)*0.5f;
+ real32 x234 = (x23 + x34)*0.5f, y234 = (y23 + y34)*0.5f;
+ real32 x1234 = (x123 + x234)*0.5f, y1234 = (y123 + y234)*0.5f;
+ Bezier_CubicClosestPointCasteljauStep(p, p_closest, ratio, r_closest, p_last, p_closest_dist2, x1, y1, x12, y12, x123, y123, x1234, y1234, tess_tol, level + 1);
+ Bezier_CubicClosestPointCasteljauStep(p, p_closest, ratio + pow(0.5, level+1), r_closest, p_last, p_closest_dist2, x1234, y1234, x234, y234, x34, y34, x4, y4, tess_tol, level + 1);
+ }
+}
+
+// finds the min/max bounds of the curve
+static void Bezier_CubicMinMaxCasteljauStep(v2 *p_min, v2 *p_max, real32 x1, real32 y1, real32 x2, real32 y2, real32 x3, real32 y3, real32 x4, real32 y4, real32 tess_tol, int level)
+{
+ real32 dx = x4 - x1;
+ real32 dy = y4 - y1;
+ real32 d2 = ((x2 - x4) * dy - (y2 - y4) * dx);
+ real32 d3 = ((x3 - x4) * dy - (y3 - y4) * dx);
+ d2 = (d2 >= 0) ? d2 : -d2;
+ d3 = (d3 >= 0) ? d3 : -d3;
+ if ((d2 + d3) * (d2 + d3) < tess_tol * (dx * dx + dy * dy))
+ {
+ v2 p_current = V2(x4, y4);
+ if (p_current.x < p_min->x) {
+ p_min->x = p_current.x;
+ }
+ if (p_current.y < p_min->y) {
+ p_min->y = p_current.y;
+ }
+ if (p_current.x > p_max->x) {
+ p_max->x = p_current.x;
+ }
+ if (p_current.y > p_max->y) {
+ p_max->y = p_current.y;
+ }
+ }
+ else if (level < 10)
+ {
+ real32 x12 = (x1 + x2)*0.5f, y12 = (y1 + y2)*0.5f;
+ real32 x23 = (x2 + x3)*0.5f, y23 = (y2 + y3)*0.5f;
+ real32 x34 = (x3 + x4)*0.5f, y34 = (y3 + y4)*0.5f;
+ real32 x123 = (x12 + x23)*0.5f, y123 = (y12 + y23)*0.5f;
+ real32 x234 = (x23 + x34)*0.5f, y234 = (y23 + y34)*0.5f;
+ real32 x1234 = (x123 + x234)*0.5f, y1234 = (y123 + y234)*0.5f;
+ Bezier_CubicMinMaxCasteljauStep(p_min, p_max, x1, y1, x12, y12, x123, y123, x1234, y1234, tess_tol, level + 1);
+ Bezier_CubicMinMaxCasteljauStep(p_min, p_max, x1234, y1234, x234, y234, x34, y34, x4, y4, tess_tol, level + 1);
+ }
+}
+
+// return all points
+static void Bezier_CubicCalcPointsCasteljauStep(void *Data, uint32 *Increment, real32 x1, real32 y1, real32 x2, real32 y2, real32 x3, real32 y3, real32 x4, real32 y4, real32 tess_tol, int level)
+{
+ real32 dx = x4 - x1;
+ real32 dy = y4 - y1;
+ real32 d2 = ((x2 - x4) * dy - (y2 - y4) * dx);
+ real32 d3 = ((x3 - x4) * dy - (y3 - y4) * dx);
+ d2 = (d2 >= 0) ? d2 : -d2;
+ d3 = (d3 >= 0) ? d3 : -d3;
+ if ((d2 + d3) * (d2 + d3) < tess_tol * (dx * dx + dy * dy))
+ {
+ *((real32 *)Data + *Increment*3) = x4;
+ *((real32 *)Data + *Increment*3 + 1) = y4;
+ *((real32 *)Data + *Increment*3 + 2) = 0;
+ *Increment += 1;
+ }
+ else if (level < 10)
+ {
+ real32 x12 = (x1 + x2)*0.5f, y12 = (y1 + y2)*0.5f;
+ real32 x23 = (x2 + x3)*0.5f, y23 = (y2 + y3)*0.5f;
+ real32 x34 = (x3 + x4)*0.5f, y34 = (y3 + y4)*0.5f;
+ real32 x123 = (x12 + x23)*0.5f, y123 = (y12 + y23)*0.5f;
+ real32 x234 = (x23 + x34)*0.5f, y234 = (y23 + y34)*0.5f;
+ real32 x1234 = (x123 + x234)*0.5f, y1234 = (y123 + y234)*0.5f;
+ Bezier_CubicCalcPointsCasteljauStep(Data, Increment, x1, y1, x12, y12, x123, y123, x1234, y1234, tess_tol, level + 1);
+ Bezier_CubicCalcPointsCasteljauStep(Data, Increment, x1234, y1234, x234, y234, x34, y34, x4, y4, tess_tol, level + 1);
+ }
+}
+
+real32 Bezier_CubicRatioOfPoint(v2 p1, v2 p2, v2 p3, v2 p4, v2 p)
+{
+ real32 tess_tol = TESS_TOL;
+ v2 p_last = p1;
+ v2 p_closest;
+ real32 p_closest_dist2 = FLT_MAX;
+ real32 ratio = 0;
+ Bezier_CubicClosestPointCasteljauStep(p, &p_closest, 0, &ratio, &p_last, &p_closest_dist2, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y, p4.x, p4.y, tess_tol, 0);
+ return ratio;
+}
+
+void Bezier_CubicCalcPoints(v2 p1, v2 p2, v2 p3, v2 p4, void *Data, uint32 *Increment)
+{
+ real32 tess_tol = TESS_TOL;
+ void *Pointer = Data;
+ Bezier_CubicCalcPointsCasteljauStep(Pointer, Increment, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y, p4.x, p4.y, tess_tol, 0);
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-09-20 07:27:35 +0000