Commit: 5ea27bec1fc1e65ce85cccd3079883a41970cd6c
Author: Campbell Barton
Date:   Tue Jun 14 16:47:05 2016 +1000
Branches: master
https://developer.blender.org/rB5ea27bec1fc1e65ce85cccd3079883a41970cd6c

BMesh Decimate: use doubles to calculate optimized position

This allows the error threshold for calculating the optimized location to be 
much lower.

Resolves visible artifacts w/ 1m-tri happy-buddha example.

===================================================================

M       source/blender/blenlib/BLI_quadric.h
M       source/blender/blenlib/intern/quadric.c
M       source/blender/bmesh/tools/bmesh_decimate_collapse.c

===================================================================

diff --git a/source/blender/blenlib/BLI_quadric.h 
b/source/blender/blenlib/BLI_quadric.h
index eaf9c7a..d46a221 100644
--- a/source/blender/blenlib/BLI_quadric.h
+++ b/source/blender/blenlib/BLI_quadric.h
@@ -39,8 +39,7 @@ typedef struct Quadric {
 
 /* conversion */
 void  BLI_quadric_from_plane(Quadric *q, const double v[4]);
-void  BLI_quadric_to_tensor_m3(const Quadric *q, float m[3][3]);
-void  BLI_quadric_to_vector_v3(const Quadric *q, float v[3]);
+void  BLI_quadric_to_vector_v3(const Quadric *q, double v[3]);
 
 void  BLI_quadric_clear(Quadric *q);
 
@@ -50,7 +49,7 @@ void  BLI_quadric_add_qu_ququ(Quadric *r, const Quadric *a, 
const Quadric *b);
 void  BLI_quadric_mul(Quadric *a, const double scalar);
 
 /* solve */
-double BLI_quadric_evaluate(const Quadric *q, const float v_fl[3]);
-bool  BLI_quadric_optimize(const Quadric *q, float v[3], const float epsilon);
+double BLI_quadric_evaluate(const Quadric *q, const double v[3]);
+bool   BLI_quadric_optimize(const Quadric *q, double v[3], const double 
epsilon);
 
 #endif /* __BLI_QUADRIC_H__ */
diff --git a/source/blender/blenlib/intern/quadric.c 
b/source/blender/blenlib/intern/quadric.c
index 588cd9c..c9d2749 100644
--- a/source/blender/blenlib/intern/quadric.c
+++ b/source/blender/blenlib/intern/quadric.c
@@ -63,26 +63,68 @@ void BLI_quadric_from_plane(Quadric *q, const double v[4])
        q->d2 = v[3] * v[3];
 }
 
-void BLI_quadric_to_tensor_m3(const Quadric *q, float m[3][3])
+#if 0  /* UNUSED */
+
+static void quadric_to_tensor_m3(const Quadric *q, double m[3][3])
 {
-       m[0][0] = (float)q->a2;
-       m[0][1] = (float)q->ab;
-       m[0][2] = (float)q->ac;
+       m[0][0] = q->a2;
+       m[0][1] = q->ab;
+       m[0][2] = q->ac;
 
-       m[1][0] = (float)q->ab;
-       m[1][1] = (float)q->b2;
-       m[1][2] = (float)q->bc;
+       m[1][0] = q->ab;
+       m[1][1] = q->b2;
+       m[1][2] = q->bc;
 
-       m[2][0] = (float)q->ac;
-       m[2][1] = (float)q->bc;
-       m[2][2] = (float)q->c2;
+       m[2][0] = q->ac;
+       m[2][1] = q->bc;
+       m[2][2] = q->c2;
 }
 
-void BLI_quadric_to_vector_v3(const Quadric *q, float v[3])
+#endif
+
+/**
+ * Inline inverse matrix creation.
+ * Equivalent of:
+ *
+ * \code{.c}
+ * quadric_to_tensor_m3(q, m);
+ * invert_m3_db(m, eps);
+ * \endcode
+ */
+static bool quadric_to_tensor_m3_inverse(const Quadric *q, double m[3][3], 
double epsilon)
 {
-       v[0] = (float)q->ad;
-       v[1] = (float)q->bd;
-       v[2] = (float)q->cd;
+       const double det =
+               (q->a2 * (q->b2 * q->c2 - q->bc * q->bc) -
+                q->ab * (q->ab * q->c2 - q->ac * q->bc) +
+                q->ac * (q->ab * q->bc - q->ac * q->b2));
+
+       if (fabs(det) > epsilon) {
+               const double invdet = 1.0 / det;
+
+               m[0][0] = (q->b2 * q->c2 - q->bc * q->bc) * invdet;
+               m[1][0] = (q->bc * q->ac - q->ab * q->c2) * invdet;
+               m[2][0] = (q->ab * q->bc - q->b2 * q->ac) * invdet;
+
+               m[0][1] = (q->ac * q->bc - q->ab * q->c2) * invdet;
+               m[1][1] = (q->a2 * q->c2 - q->ac * q->ac) * invdet;
+               m[2][1] = (q->ab * q->ac - q->a2 * q->bc) * invdet;
+
+               m[0][2] = (q->ab * q->bc - q->ac * q->b2) * invdet;
+               m[1][2] = (q->ac * q->ab - q->a2 * q->bc) * invdet;
+               m[2][2] = (q->a2 * q->b2 - q->ab * q->ab) * invdet;
+
+               return true;
+       }
+       else {
+               return false;
+       }
+}
+
+void BLI_quadric_to_vector_v3(const Quadric *q, double v[3])
+{
+       v[0] = q->ad;
+       v[1] = q->bd;
+       v[2] = q->cd;
 }
 
 void BLI_quadric_clear(Quadric *q)
@@ -105,26 +147,22 @@ void BLI_quadric_mul(Quadric *a, const double scalar)
        mul_vn_db((double *)a, QUADRIC_FLT_TOT, scalar);
 }
 
-double BLI_quadric_evaluate(const Quadric *q, const float v_fl[3])
+double BLI_quadric_evaluate(const Quadric *q, const double v[3])
 {
-       const double v[3] = {UNPACK3(v_fl)};
        return ((q->a2 * v[0] * v[0]) + (q->ab * 2 * v[0] * v[1]) + (q->ac * 2 
* v[0] * v[2]) + (q->ad * 2 * v[0]) +
                (q->b2 * v[1] * v[1]) + (q->bc * 2 * v[1] * v[2]) + (q->bd * 2 
* v[1]) +
                (q->c2 * v[2] * v[2]) + (q->cd * 2 * v[2]) +
                (q->d2));
 }
 
-bool BLI_quadric_optimize(const Quadric *q, float v[3], const float epsilon)
+bool BLI_quadric_optimize(const Quadric *q, double v[3], const double epsilon)
 {
-       float m[3][3];
+       double m[3][3];
 
-       BLI_quadric_to_tensor_m3(q, m);
-
-       if (invert_m3_ex(m, epsilon)) {
+       if (quadric_to_tensor_m3_inverse(q, m, epsilon)) {
                BLI_quadric_to_vector_v3(q, v);
-               mul_m3_v3(m, v);
-               negate_v3(v);
-
+               mul_m3_v3_db(m, v);
+               negate_v3_db(v);
                return true;
        }
        else {
diff --git a/source/blender/bmesh/tools/bmesh_decimate_collapse.c 
b/source/blender/bmesh/tools/bmesh_decimate_collapse.c
index fe8b132..3ea7dae 100644
--- a/source/blender/bmesh/tools/bmesh_decimate_collapse.c
+++ b/source/blender/bmesh/tools/bmesh_decimate_collapse.c
@@ -68,7 +68,9 @@
 #endif
 
 #define BOUNDARY_PRESERVE_WEIGHT 100.0f
-#define OPTIMIZE_EPS 0.01f  /* FLT_EPSILON is too small, see [#33106] */
+/* Uses double precision, impacts behavior on near-flat surfaces,
+ * cane give issues with very small faces. 1e-2 is too big, see: T48154. */
+#define OPTIMIZE_EPS 1e-8
 #define COST_INVALID FLT_MAX
 
 typedef enum CD_UseFlag {
@@ -140,8 +142,8 @@ static void bm_decim_build_quadrics(BMesh *bm, Quadric 
*vquadrics)
 }
 
 
-static void bm_decim_calc_target_co(
-        BMEdge *e, float optimize_co[3],
+static void bm_decim_calc_target_co_db(
+        BMEdge *e, double optimize_co[3],
         const Quadric *vquadrics)
 {
        /* compute an edge contraction target for edge 'e'
@@ -158,10 +160,22 @@ static void bm_decim_calc_target_co(
                return;  /* all is good */
        }
        else {
-               mid_v3_v3v3(optimize_co, e->v1->co, e->v2->co);
+               optimize_co[0] = 0.5 * ((double)e->v1->co[0] + 
(double)e->v2->co[0]);
+               optimize_co[1] = 0.5 * ((double)e->v1->co[1] + 
(double)e->v2->co[1]);
+               optimize_co[2] = 0.5 * ((double)e->v1->co[2] + 
(double)e->v2->co[2]);
        }
 }
 
+static void bm_decim_calc_target_co_fl(
+        BMEdge *e, float optimize_co[3],
+        const Quadric *vquadrics)
+{
+       double optimize_co_db[3];
+       bm_decim_calc_target_co_db(e, optimize_co_db, vquadrics);
+       copy_v3fl_v3db(optimize_co, optimize_co_db);
+}
+
+
 static bool bm_edge_collapse_is_degenerate_flip(BMEdge *e, const float 
optimize_co[3])
 {
        BMIter liter;
@@ -240,8 +254,6 @@ static void bm_decim_build_edge_cost_single(
         const float *vweights, const float vweight_factor,
         Heap *eheap, HeapNode **eheap_table)
 {
-       const Quadric *q1, *q2;
-       float optimize_co[3];
        float cost;
 
        if (eheap_table[BM_elem_index_get(e)]) {
@@ -279,15 +291,17 @@ static void bm_decim_build_edge_cost_single(
        }
        /* end sanity check */
 
+       {
+               double optimize_co[3];
+               bm_decim_calc_target_co_db(e, optimize_co, vquadrics);
 
-       bm_decim_calc_target_co(e, optimize_co, vquadrics);
-
-       q1 = &vquadrics[BM_elem_index_get(e->v1)];
-       q2 = &vquadrics[BM_elem_index_get(e->v2)];
-
-       cost = (BLI_quadric_evaluate(q1, optimize_co) +
-               BLI_quadric_evaluate(q2, optimize_co));
+               const Quadric *q1, *q2;
+               q1 = &vquadrics[BM_elem_index_get(e->v1)];
+               q2 = &vquadrics[BM_elem_index_get(e->v2)];
 
+               cost = (BLI_quadric_evaluate(q1, optimize_co) +
+                       BLI_quadric_evaluate(q2, optimize_co));
+       }
 
        /* note, 'cost' shouldn't be negative but happens sometimes with small 
values.
         * this can cause faces that make up a flat surface to over-collapse, 
see [#37121] */
@@ -1155,7 +1169,7 @@ static bool bm_decim_edge_collapse(
                        return false;
                }
 
-               bm_decim_calc_target_co(e, optimize_co, vquadrics);
+               bm_decim_calc_target_co_fl(e, optimize_co, vquadrics);
 
                /* check if this would result in an overlapping face */
                if (UNLIKELY(bm_edge_collapse_is_degenerate_flip(e, 
optimize_co))) {
@@ -1426,7 +1440,7 @@ void BM_mesh_decimate_collapse(
                                        goto invalidate;
                                }
 
-                               bm_decim_calc_target_co(e, optimize_co, 
vquadrics);
+                               bm_decim_calc_target_co_fl(e, optimize_co, 
vquadrics);
 
                                if (e_index_mirr == e_index) {
                                        optimize_co[symmetry_axis] = 0.0f;

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