diff --git a/include/merian-shaders/common.glsl b/include/merian-shaders/common.glsl
index df83939..9278024 100644
--- a/include/merian-shaders/common.glsl
+++ b/include/merian-shaders/common.glsl
@@ -3,7 +3,10 @@
 
 #define M_PI   3.14159265358979323846
 #define TWO_PI 6.283185307179586
+#define FOUR_PI 12.566370614359172
 #define INV_PI 0.3183098861837907
+#define INV_TWO_PI 0.15915494309189535
+#define INV_FOUR_PI 0.07957747154594767
 #define INV_SQRT_TWO_PI 0.3989422804014327
 
 // returns 1/x if x > 0 else 1.
diff --git a/include/merian-shaders/von_mises_fisher.glsl b/include/merian-shaders/von_mises_fisher.glsl
index 33299b0..53308d1 100644
--- a/include/merian-shaders/von_mises_fisher.glsl
+++ b/include/merian-shaders/von_mises_fisher.glsl
@@ -8,14 +8,14 @@
 
 // numerically robust von Mises Fisher lobe
 float vmf_pdf(const float kappa, const float dotmu) {
-    if (kappa < 1e-4) return 1.0 / (4.0 * M_PI);
-    return kappa / (2.0 * M_PI * (1.0 - exp(-2.0 * kappa))) * exp(kappa * (dotmu - 1.0));
+    if (kappa < 1e-4) return INV_FOUR_PI;
+    return kappa / (TWO_PI * (1.0 - exp(-2.0 * kappa))) * exp(kappa * (dotmu - 1.0));
 }
 
 // see wenzel's doc on numerically stable expression for vmm
 vec3 vmf_sample(const float kappa, const vec2 random) {
-    const float w = 1.0 + log(random.x + (1.0-random.x) * exp(-2.0 * kappa)) / kappa;
-    const vec2 v = vec2(sin(2.0 * M_PI * random.y), cos(2.0 * M_PI * random.y));
+    const float w = 1.0 + log(random.x + (1.0 - random.x) * exp(-2.0 * kappa)) / kappa;
+    const vec2 v = vec2(sin(TWO_PI * random.y), cos(TWO_PI * random.y));
     return vec3(sqrt(1.0 - w * w) * v, w);
 }
 
@@ -26,7 +26,7 @@ vec3 vmf_sample(const vec3 z, const float kappa, const vec2 random) {
 
 // compute concentration parameter for given maximum density x
 float vmf_get_kappa(const float pdf) {
-    if (pdf > 0.795) return 2.0 * M_PI * pdf;
+    if (pdf > 0.795) return TWO_PI * pdf;
     return max(1e-5, (168.479 * pdf * pdf + 16.4585 * pdf - 2.39942) / (-1.12718 * pdf * pdf + 29.1433 * pdf + 1.0));
 }