Add dual paraboloid transform.

src/nvtt/TexImage.cpp

@@ -1593,6 +1593,31 @@ void TexImage::transformNormals(NormalTransform xform)
             n.y = n.y * t;
             n.z = 0.0f;
         }
+        else if (xform == NormalTransform_DualParaboloid) {
+            // Use Newton's method to solve equation:
+            // f(t) = 1 - zt - (x^2+y^2)t^2 + x^2y^2t^4 = 0
+            // f'(t) = - z - 2(x^2+y^2)t + 4x^2y^2t^3
+
+            // Initial approximation:
+            float a = (n.x * n.x) + (n.y * n.y);
+            float b = n.z;
+            float c = -1.0f;
+            float discriminant = b * b - 4.0f * a * c;
+            float t = (-b + sqrtf(discriminant)) / (2.0f * a);
+
+            float d = fabs(n.z * t - (1 - n.x*n.x*t*t) * (1 - n.y*n.y*t*t));
+
+            while (d > 0.0001) {
+                float ft = 1 - n.z * t - (n.x*n.x + n.y*n.y)*t*t + n.x*n.x*n.y*n.y*t*t*t*t;
+                float fit = - n.z - 2*(n.x*n.x + n.y*n.y)*t + 4*n.x*n.x*n.y*n.y*t*t*t;
+                t -= ft / fit;
+                d = fabs(n.z * t - (1 - n.x*n.x*t*t) * (1 - n.y*n.y*t*t));
+            };
+
+            n.x = n.x * t;
+            n.y = n.y * t;
+            n.z = 0.0f;
+        }
 
         x = n.x;
         y = n.y;
@@ -1632,6 +1657,12 @@ void TexImage::reconstructNormals(NormalTransform xform)
             n.z = 1.0f - nv::clamp(n.x * n.x + n.y * n.y, 0.0f, 1.0f);
             n = normalizeSafe(n, Vector3(0.0f), 0.0f);
         }
+        else if (xform == NormalTransform_DualParaboloid) {
+            n.x = n.x;
+            n.y = n.y;
+            n.z = nv::clamp((1 - n.x * n.x) * (1 - n.y * n.y), 0.0f, 1.0f);
+            n = normalizeSafe(n, Vector3(0.0f), 0.0f);
+        }
 
         x = n.x;
         y = n.y;

src/nvtt/nvtt.h

@@ -391,6 +391,7 @@ namespace nvtt
         NormalTransform_Orthographic,
         NormalTransform_Stereographic,
         NormalTransform_Paraboloid,
+        NormalTransform_DualParaboloid,
     };
 
     /// A texture mipmap.

src/nvtt/tests/testsuite.cpp

@@ -185,6 +185,7 @@ enum Mode {
     Mode_BC5_Normal,
     Mode_BC5_Normal_Stereographic,
     Mode_BC5_Normal_Paraboloid,
+    Mode_BC5_Normal_DualParaboloid,
     Mode_Count
 };
 static const char * s_modeNames[] = {
@@ -201,6 +202,7 @@ static const char * s_modeNames[] = {
     "BC5-Normal",   // Mode_BC5_Normal,
     "BC5-Normal-Stereographic",     // Mode_BC5_Normal_Stereographic,
     "BC5-Normal-Paraboloid",        // Mode_BC5_Normal_Paraboloid,
+    "BC5-Normal-DualParaboloid",    // Mode_BC5_Normal_DualParaboloid,
 };
 nvStaticCheck(NV_ARRAY_SIZE(s_modeNames) == Mode_Count);
 
@@ -213,7 +215,7 @@ static Test s_imageTests[] = {
     {"Color", 3, {Mode_BC1, Mode_BC3_YCoCg, Mode_BC3_RGBM, Mode_BC3_LUVW}},
     {"Alpha", 3, {Mode_BC1_Alpha, Mode_BC2_Alpha, Mode_BC3_Alpha}},
     //{"Normal", 3, {Mode_BC1_Normal, Mode_BC3_Normal, Mode_BC5_Normal}},
-    {"Normal", 3, {Mode_BC5_Normal, Mode_BC5_Normal_Stereographic, Mode_BC5_Normal_Paraboloid}},
+    {"Normal", 4, {Mode_BC5_Normal_DualParaboloid, Mode_BC5_Normal, Mode_BC5_Normal_Stereographic, Mode_BC5_Normal_Paraboloid}},
     {"Lightmap", 4, {Mode_BC1, Mode_BC3_YCoCg, Mode_BC3_RGBM, Mode_BC3_RGBS}},
 };
 const int s_imageTestCount = ARRAY_SIZE(s_imageTests);
@@ -404,7 +406,7 @@ int main(int argc, char *argv[])
         printf("  -dec x         \tDecompressor.\n");
         printf("    0:           \tReference (D3D10).\n");
         printf("    1:           \tReference (D3D9).\n");
-        printf("    1:           \tNVIDIA.\n");
+        printf("    2:           \tNVIDIA.\n");
 
         printf("Compression options:\n");
         printf("  -fast          \tFast compression.\n");
@@ -551,7 +553,7 @@ int main(int argc, char *argv[])
         else if (mode == Mode_BC3_Normal) {
             format = nvtt::Format_BC3n;
         }
-        else if (mode == Mode_BC5_Normal) {
+        else if (mode == Mode_BC5_Normal || mode == Mode_BC5_Normal_Stereographic || mode == Mode_BC5_Normal_Paraboloid || mode == Mode_BC5_Normal_DualParaboloid) {
             format = nvtt::Format_BC5;
         }
         
@@ -661,6 +663,9 @@ int main(int argc, char *argv[])
             else if (mode == Mode_BC5_Normal_Paraboloid) {
                 tmp.transformNormals(nvtt::NormalTransform_Paraboloid);
             }
+            else if (mode == Mode_BC5_Normal_DualParaboloid) {
+                tmp.transformNormals(nvtt::NormalTransform_DualParaboloid);
+            }
 
 
             printf("Compressing: \t'%s'\n", set.fileNames[i]);
@@ -735,6 +740,9 @@ int main(int argc, char *argv[])
             else if (mode == Mode_BC5_Normal_Paraboloid) {
                 img_out.reconstructNormals(nvtt::NormalTransform_Paraboloid);
             }
+            else if (mode == Mode_BC5_Normal_DualParaboloid) {
+                img_out.reconstructNormals(nvtt::NormalTransform_DualParaboloid);
+            }
 
             nvtt::TexImage diff = nvtt::diff(img, img_out, 1.0f);