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+#ifndef __MATH_INC
+#define __MATH_INC
+
+#define PI 3.14159265358979f
+#define RCP_PI (1.0f / PI)
+
+// Wrap a dot product. Assume it's already clamped.
+// At k=0, you get standard lambertian shading.
+// At k=0.5, you get half-lambertian shading.
+// At k=1.0, you get flat shading.
+// k must be on [0, 1].
+// Energy preserving, within some small bound.
+float wrapDotProduct(float XoY, float k) {
+  float lambertian = XoY;
+  float half_lambertian = pow(max(1e-4, (XoY + 0.5f) / (1.0f + 0.5f)), 2);
+  float flat = RCP_PI;
+
+  if (k < 0.5) {
+    return lerp(lambertian, half_lambertian, k * 2.0f);
+  } else {
+    return lerp(half_lambertian, flat, k * 2.0f - 1.0f);
+  }
+}
+
+#endif  // __MATH_INC
+