some ray marching

1 files changed, 39 insertions, 4 deletions

diff --git a/math.cginc b/math.cginc
index 4cfed67..58a9c08 100644
--- a/math.cginc
+++ b/math.cginc
@@ -1,10 +1,21 @@
 #ifndef __MATH_INC
 #define __MATH_INC
 
-#define PI 3.14159265358979f
-#define RCP_PI (1.0f / PI)
-#define TAU (2.0f * PI)
-#define SQRT_3 1.73205081f
+#define PI              3.14159265358979323846264f
+#define TAU             (2.0f * PI)
+#define HALF_PI         (PI * 0.5f)
+#define RCP_PI          (1.0f / PI)
+#define RCP_TAU         (1.0f / TAU)
+#define PHI             1.618033989f
+#define RCP_PHI         0.618033989f
+#define SQRT_2          1.414213562f
+#define SQRT_2_RCP      0.707106781f
+#define RCP_SQRT_2      0.707106781f
+#define RCP_SQRT_3      0.577350269f
+#define TWO_OVER_THREE  0.6666666666666666f
+#define SQRT_3          1.73205081f
+#define SQRT_3_OVER_2   0.8660254037844386f
+#define EULERS_CONSTANT 2.718281828f
 
 float sin_noise_3d(float3 uvw) {
   return sin(uvw[0]) * sin(uvw[1]) * sin(uvw[2]);
@@ -39,5 +50,29 @@ float wrapDotProduct(float XoY, float k) {
   }
 }
 
+// Vector rotation with a quaternion
+// https://blog.molecular-matters.com/2013/05/24/a-faster-quaternion-vector-multiplication/
+float3 rotate_vector(float3 v, float4 q)
+{
+  float3 t = 2.0 * cross(q.xyz, v);
+  return v + q.w * t + cross(q.xyz, t);
+}
+
+// Cartesian to cube hexagonal coordinates.
+// Based on this: https://backdrifting.net/post/064_hex_grids
+float3 cart_to_hex(float2 cart) {
+  float p = cart.x;
+  float q = dot(cart, float2(0.5f, SQRT_3_OVER_2));
+  float r = dot(cart, float2(0.5f, -SQRT_3_OVER_2));
+
+  return float3(p, q, r) * TWO_OVER_THREE;
+}
+
+float2 hex_to_cart(float3 cart) {
+  return float2(
+      cart[0] + (cart[1] + cart[2]) * 0.5f,
+      (cart[1] - cart[2]) * SQRT_3_OVER_2);
+}
+
 #endif  // __MATH_INC