Bound the shadow frustum more closely.

3 files changed, 53 insertions, 9 deletions

diff --git a/glass.h b/glass.h
index d122e86..f3dc795 100644
--- a/glass.h
+++ b/glass.h
@@ -84,6 +84,9 @@ void init_m4_perspective(float *mat4, float fovy, float aspect,
 void print_m4(const float *mat4, const char *name);
 void print_GLUvec4(char *desc, const GLUvec4 *vec);
 void print_GLUmat4(char *desc, const GLUmat4 *m);
+void make_sphere_frustum(GLUmat4 *mat,
+			 GLUvec4 *center,
+			 float radius);
 
 /* load_texture.c */
 GLuint load_texture_rgb(const char *filename);
diff --git a/matrix.c b/matrix.c
index 8aa02e6..f81d830 100644
--- a/matrix.c
+++ b/matrix.c
@@ -30,6 +30,7 @@
 #include <stdlib.h>
 #include <math.h>
 #include <string.h>
+#include <assert.h>
 
 #include "glass.h"
 
@@ -212,3 +213,50 @@ print_GLUmat4(char *desc, const GLUmat4 *m)
 		       i == 0 ? "" : "}");
 	}
 }
+
+static float length_3v(GLUvec4 *vec)
+{
+	return sqrt(vec->values[0] * vec->values[0] +
+		    vec->values[1] * vec->values[1] +
+		    vec->values[2] * vec->values[2]);
+}
+
+void
+make_sphere_frustum(GLUmat4 *mat,
+		    GLUvec4 *center,
+		    float radius)
+{
+	float near_radius;
+	float center_distance = length_3v(center);
+	float near = center_distance - radius;
+	float far = center_distance + radius;
+
+	assert(near > 0);
+
+	/* We want to make a frustum that just bounds the sphere.
+	 * Obviously the near/far will the length of the vector to the center
+	 * plus or minus the radius. For gluFrustum6, though, the l/r/t/b values
+	 * are on the near plane, so we have to figure out where a line from
+	 * the eye (0,0,0) tangent to the sphere ends up intersecting the near
+	 * plane.
+	 *
+	 * Given hideous ASCII art:
+	 *      ___
+	 *     / \/\__ a = sqrt(n*n+2rn)
+	 *    / r/\|t \__
+	 *   |  /__|_____\
+	 *   |   r |  n
+	 *    \   /
+	 *     \_/
+	 *
+	 * then tan θ = r/a = t/n.
+	 * so t = nr/a = nr/sqrt(n*n+2rn).
+	 */
+
+	near_radius = near * radius / sqrt(near * near + 2.0 * near * radius);
+
+	gluFrustum6(mat,
+		    -near_radius, near_radius,
+		    -near_radius, near_radius,
+		    near, far);
+}
diff --git a/shadow_map.c b/shadow_map.c
index 38fc0fb..073ec6a 100644
--- a/shadow_map.c
+++ b/shadow_map.c
@@ -50,7 +50,6 @@ calculate_light_projection(void)
 	GLUvec4 light_up;
 	GLUmat4 temp;
 	GLUvec4 light_to_rings;
-	float light_distance_to_rings;
 
 	/* Wrong.  So wrong. */
 	light_up.values[0] = 1.0;
@@ -69,9 +68,6 @@ calculate_light_projection(void)
 	 */
 	gluSub4v_4v(&light_to_rings,
 		    &ring_bounding_sphere_center_world, &light_world);
-	light_distance_to_rings = gluLength4v(&light_to_rings);
-
-	assert(light_distance_to_rings > ring_bounding_sphere_radius);
 
 	/* Transform for looking from they eye's point of view at the pile of
 	 * rings.
@@ -80,11 +76,8 @@ calculate_light_projection(void)
 		    &light_world,
 		    &ring_bounding_sphere_center_world,
 		    &light_up);
-	gluFrustum6(&temp,
-		    -ring_bounding_sphere_radius, ring_bounding_sphere_radius,
-		    -ring_bounding_sphere_radius, ring_bounding_sphere_radius,
-		    light_distance_to_rings - ring_bounding_sphere_radius,
-		    light_distance_to_rings + ring_bounding_sphere_radius);
+	make_sphere_frustum(&temp, &light_to_rings,
+			    ring_bounding_sphere_radius);
 	/*print_GLUmat4("frustum", &temp);*/
 	gluMult4m_4m(&world_to_light_ndc, &temp, &world_to_light_eye);
 }