Math Lib: add dist_squared_to_line_v2, avoids sqrt in scanfill and 3d-text

4 files changed, 52 insertions, 18 deletions

diff --git a/source/blender/blenlib/BLI_math_geom.h b/source/blender/blenlib/BLI_math_geom.h
index 4f41ac86a0e..e99f89036b3 100644
--- a/source/blender/blenlib/BLI_math_geom.h
+++ b/source/blender/blenlib/BLI_math_geom.h
@@ -80,7 +80,8 @@ int is_quad_convex_v2(const float v1[2], const float v2[2], const float v3[2], c
 
 /********************************* Distance **********************************/
 
-float dist_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
+float dist_squared_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
+float         dist_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
 float dist_squared_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
 float         dist_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
 void closest_to_line_segment_v2(float closest[2], const float p[2], const float l1[2], const float l2[2]);
@@ -89,7 +90,8 @@ float dist_squared_to_plane_v3(const float p[3], const float plane[4]);
 float dist_to_plane_v3(const float p[3], const float plane[4]);
 float dist_squared_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
 float         dist_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
-float dist_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
+float dist_squared_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
+float         dist_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
 float closest_to_line_v3(float r[3], const float p[3], const float l1[3], const float l2[3]);
 float closest_to_line_v2(float r[2], const float p[2], const float l1[2], const float l2[2]);
 void closest_to_line_segment_v3(float r[3], const float p[3], const float l1[3], const float l2[3]);
diff --git a/source/blender/blenlib/intern/freetypefont.c b/source/blender/blenlib/intern/freetypefont.c
index 10d574e56b4..4f703d2d148 100644
--- a/source/blender/blenlib/intern/freetypefont.c
+++ b/source/blender/blenlib/intern/freetypefont.c
@@ -64,6 +64,8 @@ static FT_Error err;
 
 static void freetypechar_to_vchar(FT_Face face, FT_ULong charcode, VFontData *vfd)
 {
+	const float eps = 0.0001f;
+	const float eps_sq = eps * eps;
 	/* Blender */
 	struct Nurb *nu;
 	struct VChar *che;
@@ -260,18 +262,19 @@ static void freetypechar_to_vchar(FT_Face face, FT_ULong charcode, VFontData *vf
 					}
 
 					/* get the handles that are aligned, tricky...
-					 * dist_to_line_v2, check if the three beztriple points are on one line
-					 * len_squared_v2v2, see if there's a distance between the three points
-					 * len_squared_v2v2 again, to check the angle between the handles
-					 * finally, check if one of them is a vector handle */
+					 * - check if one of them is a vector handle.
+					 * - dist_squared_to_line_v2, check if the three beztriple points are on one line
+					 * - len_squared_v2v2, see if there's a distance between the three points
+					 * - len_squared_v2v2 again, to check the angle between the handles
+					 */
 					if ((bezt->h1 != HD_VECT && bezt->h2 != HD_VECT) &&
-					    (dist_to_line_v2(bezt->vec[0], bezt->vec[1], bezt->vec[2]) < 0.001f) &&
-					    (len_squared_v2v2(bezt->vec[0], bezt->vec[1]) > 0.0001f * 0.0001f) &&
-					    (len_squared_v2v2(bezt->vec[1], bezt->vec[2]) > 0.0001f * 0.0001f) &&
-					    (len_squared_v2v2(bezt->vec[0], bezt->vec[2]) > 0.0002f * 0.0001f) &&
+					    (dist_squared_to_line_v2(bezt->vec[0], bezt->vec[1], bezt->vec[2]) < (0.001f * 0.001f)) &&
+					    (len_squared_v2v2(bezt->vec[0], bezt->vec[1]) > eps_sq) &&
+					    (len_squared_v2v2(bezt->vec[1], bezt->vec[2]) > eps_sq) &&
+					    (len_squared_v2v2(bezt->vec[0], bezt->vec[2]) > eps_sq) &&
 					    (len_squared_v2v2(bezt->vec[0], bezt->vec[2]) >
 					     max_ff(len_squared_v2v2(bezt->vec[0], bezt->vec[1]),
-					          len_squared_v2v2(bezt->vec[1], bezt->vec[2]))))
+					            len_squared_v2v2(bezt->vec[1], bezt->vec[2]))))
 					{
 						bezt->h1 = bezt->h2 = HD_ALIGN;
 					}
diff --git a/source/blender/blenlib/intern/math_geom.c b/source/blender/blenlib/intern/math_geom.c
index 1d03bf42f83..833a08cec60 100644
--- a/source/blender/blenlib/intern/math_geom.c
+++ b/source/blender/blenlib/intern/math_geom.c
@@ -219,17 +219,41 @@ float volume_tetrahedron_v3(const float v1[3], const float v2[3], const float v3
 
 /* distance p to line v1-v2
  * using Hesse formula, NO LINE PIECE! */
+float dist_squared_to_line_v2(const float p[2], const float l1[2], const float l2[2])
+{
+	float a[2], deler;
+
+	a[0] = l1[1] - l2[1];
+	a[1] = l2[0] - l1[0];
+
+	deler = len_squared_v2(a);
+
+	if (deler != 0.0f) {
+		float f = ((p[0] - l1[0]) * a[0] +
+		           (p[1] - l1[1]) * a[1]);
+		return (f * f) / deler;
+	}
+	else {
+		return 0.0f;
+	}
+}
 float dist_to_line_v2(const float p[2], const float l1[2], const float l2[2])
 {
 	float a[2], deler;
 
 	a[0] = l1[1] - l2[1];
 	a[1] = l2[0] - l1[0];
-	deler = (float)sqrt(a[0] * a[0] + a[1] * a[1]);
-	if (deler == 0.0f) return 0;
 
-	return fabsf((p[0] - l1[0]) * a[0] + (p[1] - l1[1]) * a[1]) / deler;
+	deler = len_squared_v2(a);
 
+	if (deler != 0.0f) {
+		float f = ((p[0] - l1[0]) * a[0] +
+		           (p[1] - l1[1]) * a[1]);
+		return fabsf(f) / sqrtf(deler);
+	}
+	else {
+		return 0.0f;
+	}
 }
 
 /* distance p to line-piece v1-v2 */
@@ -350,13 +374,17 @@ float dist_to_line_segment_v3(const float p[3], const float l1[3], const float l
 	return sqrtf(dist_squared_to_line_segment_v3(p, l1, l2));
 }
 
-float dist_to_line_v3(const float v1[3], const float l1[3], const float l2[3])
+float dist_squared_to_line_v3(const float v1[3], const float l1[3], const float l2[3])
 {
 	float closest[3];
 
 	closest_to_line_v3(closest, v1, l1, l2);
 
-	return len_v3v3(closest, v1);
+	return len_squared_v3v3(closest, v1);
+}
+float dist_to_line_v3(const float v1[3], const float l1[3], const float l2[3])
+{
+	return sqrtf(dist_squared_to_line_v3(v1, l1, l2));
 }
 
 /* Adapted from "Real-Time Collision Detection" by Christer Ericson,
diff --git a/source/blender/blenlib/intern/scanfill.c b/source/blender/blenlib/intern/scanfill.c
index a292c2275c9..c4cefadb815 100644
--- a/source/blender/blenlib/intern/scanfill.c
+++ b/source/blender/blenlib/intern/scanfill.c
@@ -62,6 +62,7 @@ typedef struct ScanFillVertLink {
 /* local funcs */
 
 #define SF_EPSILON   0.00003f
+#define SF_EPSILON_SQ (SF_EPSILON * SF_EPSILON)
 
 #define SF_VERT_AVAILABLE  1  /* available - in an edge */
 #define SF_VERT_ZERO_LEN 255
@@ -374,8 +375,8 @@ static void testvertexnearedge(ScanFillContext *sf_ctx)
 					}
 					else {
 						if (boundinsideEV(eed, eve)) {
-							const float dist = dist_to_line_v2(eed->v1->xy, eed->v2->xy, eve->xy);
-							if (dist < SF_EPSILON) {
+							const float dist = dist_squared_to_line_v2(eed->v1->xy, eed->v2->xy, eve->xy);
+							if (dist < SF_EPSILON_SQ) {
 								/* new edge */
 								ed1 = BLI_scanfill_edge_add(sf_ctx, eed->v1, eve);