Math Lib: improve area calculation

- area_quad_v3 now works correctly with concave quads.
- add area_squared_*** functions, to use when comparing to avoid a sqrt().

5 files changed, 70 insertions, 46 deletions

diff --git a/source/blender/blenkernel/intern/mesh_evaluate.c b/source/blender/blenkernel/intern/mesh_evaluate.c
index 4c9e44682c3..915abdb6766 100644
--- a/source/blender/blenkernel/intern/mesh_evaluate.c
+++ b/source/blender/blenkernel/intern/mesh_evaluate.c
@@ -896,13 +896,6 @@ float BKE_mesh_calc_poly_area(MPoly *mpoly, MLoop *loopstart,
 		                   mvarray[loopstart[2].v].co
 		                   );
 	}
-	else if (mpoly->totloop == 4) {
-		return area_quad_v3(mvarray[loopstart[0].v].co,
-		                    mvarray[loopstart[1].v].co,
-		                    mvarray[loopstart[2].v].co,
-		                    mvarray[loopstart[3].v].co
-		                    );
-	}
 	else {
 		int i;
 		MLoop *l_iter = loopstart;
diff --git a/source/blender/blenlib/BLI_math_geom.h b/source/blender/blenlib/BLI_math_geom.h
index ee99f860a97..495aa6b2465 100644
--- a/source/blender/blenlib/BLI_math_geom.h
+++ b/source/blender/blenlib/BLI_math_geom.h
@@ -52,16 +52,23 @@ float normal_quad_v3(float r[3], const float a[3], const float b[3], const float
 float normal_poly_v3(float r[3], const float verts[][3], unsigned int nr);
 
 MINLINE float area_tri_v2(const float a[2], const float b[2], const float c[2]);
+MINLINE float area_squared_tri_v2(const float a[2], const float b[2], const float c[2]);
 MINLINE float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2]);
 float area_tri_v3(const float a[3], const float b[3], const float c[3]);
+float area_squared_tri_v3(const float a[3], const float b[3], const float c[3]);
 float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float normal[3]);
 float area_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
+float area_squared_quad_v3(const float a[3], const float b[3], const float c[3], const float d[3]);
 float area_poly_v3(const float verts[][3], unsigned int nr);
 float area_poly_v2(const float verts[][2], unsigned int nr);
+float area_squared_poly_v3(const float verts[][3], unsigned int nr);
+float area_squared_poly_v2(const float verts[][2], unsigned int nr);
+float area_poly_signed_v2(const float verts[][2], unsigned int nr);
 float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3]);
 
 void          cross_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3]);
 MINLINE float cross_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
+void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr);
 float cross_poly_v2(const float verts[][2], unsigned int nr);
 
 /********************************* Planes **********************************/
diff --git a/source/blender/blenlib/intern/math_geom.c b/source/blender/blenlib/intern/math_geom.c
index 59d9cf85dec..05a527c4f7a 100644
--- a/source/blender/blenlib/intern/math_geom.c
+++ b/source/blender/blenlib/intern/math_geom.c
@@ -109,58 +109,44 @@ float normal_quad_v3(float n[3], const float v1[3], const float v2[3], const flo
  */
 float normal_poly_v3(float n[3], const float verts[][3], unsigned int nr)
 {
-	const float *v_prev = verts[nr - 1];
-	const float *v_curr = verts[0];
-	unsigned int i;
-
-	zero_v3(n);
-
-	/* Newell's Method */
-	for (i = 0; i < nr; v_prev = v_curr, v_curr = verts[++i]) {
-		add_newell_cross_v3_v3v3(n, v_prev, v_curr);
-	}
-
+	cross_poly_v3(n, verts, nr);
 	return normalize_v3(n);
 }
 
-/* only convex Quadrilaterals */
 float area_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3])
 {
-	float len, vec1[3], vec2[3], n[3];
-
-	sub_v3_v3v3(vec1, v2, v1);
-	sub_v3_v3v3(vec2, v4, v1);
-	cross_v3_v3v3(n, vec1, vec2);
-	len = len_v3(n);
-
-	sub_v3_v3v3(vec1, v4, v3);
-	sub_v3_v3v3(vec2, v2, v3);
-	cross_v3_v3v3(n, vec1, vec2);
-	len += len_v3(n);
+	const float verts[4][3] = {{UNPACK3(v1)}, {UNPACK3(v2)}, {UNPACK3(v3)}, {UNPACK3(v4)}};
+	return area_poly_v3(verts, 4);
+}
 
-	return (len / 2.0f);
+float area_squared_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3])
+{
+	const float verts[4][3] = {{UNPACK3(v1)}, {UNPACK3(v2)}, {UNPACK3(v3)}, {UNPACK3(v4)}};
+	return area_squared_poly_v3(verts, 4);
 }
 
 /* Triangles */
 float area_tri_v3(const float v1[3], const float v2[3], const float v3[3])
 {
-	float vec1[3], vec2[3], n[3];
-
-	sub_v3_v3v3(vec1, v3, v2);
-	sub_v3_v3v3(vec2, v1, v2);
-	cross_v3_v3v3(n, vec1, vec2);
+	float n[3];
+	cross_tri_v3(n, v1, v2, v3);
+	return len_v3(n) * 0.5f;
+}
 
-	return len_v3(n) / 2.0f;
+float area_squared_tri_v3(const float v1[3], const float v2[3], const float v3[3])
+{
+	float n[3];
+	cross_tri_v3(n, v1, v2, v3);
+	mul_v3_fl(n, 0.5f);
+	return len_squared_v3(n);
 }
 
 float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3], const float normal[3])
 {
-	float area, vec1[3], vec2[3], n[3];
+	float area, n[3];
 
-	sub_v3_v3v3(vec1, v3, v2);
-	sub_v3_v3v3(vec2, v1, v2);
-	cross_v3_v3v3(n, vec1, vec2);
-	area = len_v3(n) / 2.0f;
+	cross_tri_v3(n, v1, v2, v3);
+	area = len_v3(n) * 0.5f;
 
 	/* negate area for flipped triangles */
 	if (dot_v3v3(n, normal) < 0.0f)
@@ -172,7 +158,17 @@ float area_tri_signed_v3(const float v1[3], const float v2[3], const float v3[3]
 float area_poly_v3(const float verts[][3], unsigned int nr)
 {
 	float n[3];
-	return normal_poly_v3(n, verts, nr) * 0.5f;
+	cross_poly_v3(n, verts, nr);
+	return len_v3(n) * 0.5f;
+}
+
+float area_squared_poly_v3(const float verts[][3], unsigned int nr)
+{
+	float n[3];
+
+	cross_poly_v3(n, verts, nr);
+	mul_v3_fl(n, 0.5f);
+	return len_squared_v3(n);
 }
 
 /**
@@ -200,11 +196,36 @@ float cross_poly_v2(const float verts[][2], unsigned int nr)
 	return cross;
 }
 
+void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr)
+{
+	const float *v_prev = verts[nr - 1];
+	const float *v_curr = verts[0];
+	unsigned int i;
+
+	zero_v3(n);
+
+	/* Newell's Method */
+	for (i = 0; i < nr; v_prev = v_curr, v_curr = verts[++i]) {
+		add_newell_cross_v3_v3v3(n, v_prev, v_curr);
+	}
+}
+
 float area_poly_v2(const float verts[][2], unsigned int nr)
 {
 	return fabsf(0.5f * cross_poly_v2(verts, nr));
 }
 
+float area_poly_signed_v2(const float verts[][2], unsigned int nr)
+{
+	return (0.5f * cross_poly_v2(verts, nr));
+}
+
+float area_squared_poly_v2(const float verts[][2], unsigned int nr)
+{
+	float area = area_poly_signed_v2(verts, nr);
+	return area * area;
+}
+
 float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3])
 {
 	float a[3], b[3], c[3], c_len;
diff --git a/source/blender/blenlib/intern/math_geom_inline.c b/source/blender/blenlib/intern/math_geom_inline.c
index 5a64ed63ecf..44b17681540 100644
--- a/source/blender/blenlib/intern/math_geom_inline.c
+++ b/source/blender/blenlib/intern/math_geom_inline.c
@@ -54,6 +54,12 @@ MINLINE float area_tri_v2(const float v1[2], const float v2[2], const float v3[2
 	return fabsf(area_tri_signed_v2(v1, v2, v3));
 }
 
+MINLINE float area_squared_tri_v2(const float v1[2], const float v2[2], const float v3[2])
+{
+	float area = area_tri_signed_v2(v1, v2, v3);
+	return area * area;
+}
+
 /****************************** Spherical Harmonics **************************/
 
 MINLINE void zero_sh(float r[9])
diff --git a/source/blender/bmesh/intern/bmesh_polygon.c b/source/blender/bmesh/intern/bmesh_polygon.c
index f2c426133c2..e4aa4bb0c0e 100644
--- a/source/blender/bmesh/intern/bmesh_polygon.c
+++ b/source/blender/bmesh/intern/bmesh_polygon.c
@@ -214,9 +214,6 @@ float BM_face_calc_area(BMFace *f)
 	if (f->len == 3) {
 		area = area_tri_v3(verts[0], verts[1], verts[2]);
 	}
-	else if (f->len == 4) {
-		area = area_quad_v3(verts[0], verts[1], verts[2], verts[3]);
-	}
 	else {
 		area = area_poly_v3((const float (*)[3])verts, f->len);
 	}