add world coordinate transformations to math library

src/math.hpp

@@ -10,9 +10,8 @@
 
 [math.hpp]
 
-For math helper functions that require only GLM primitives, especially trigonometric functions.
-Angle values are in radians. 0 is directly up on the screen in GL coordinates, and the angle increases
-clockwise.
+For math helper functions that require only GLM primitives, especially trigonometric functions. Angle values are in radians. 0 is
+directly up on the screen in GL coordinates, and the angle increases clockwise.
 
 This test of points on a square and one point below the square should print the output below.
 
@@ -235,4 +234,46 @@ namespace sb
         
         return segments;
     }
+
+    /*!
+     * @param world            world coordinates
+     * @param transformation   transformation to apply to the given world coordinates, if any
+     */
+    template<glm::length_t dimensions, typename Type, glm::qualifier qualifier>
+    glm::vec4 world_to_clip(const glm::vec<dimensions, Type, qualifier>& world, const glm::mat4& transformation = glm::mat4{1.0f})
+    {
+        /* Create a 4-D vertex with the w-coordinate normalized to 1.0f. */
+        glm::vec4 _world {world.x, world.y, 0.0f, 1.0f};
+
+        /* If a third dimension was passed, get it from the caller. */
+        if constexpr (dimensions > 2)
+        {
+            _world.z = world.z;
+        }
+
+        /* Apply projection and view transformations */
+        return transformation * _world;
+    }
+
+    /*!
+     * @param world            world coordinates
+     * @param transformation   transformation to apply to the given world coordinates, if any
+     */
+    template<glm::length_t dimensions, typename Type, glm::qualifier qualifier>
+    glm::vec3 world_to_ndc(const glm::vec<dimensions, Type, qualifier>& world, const glm::mat4& transformation = glm::mat4{1.0f})
+    {
+        glm::vec4 clip = world_to_clip(world, transformation);
+        return glm::vec3{clip.x, clip.y, clip.z} / clip.w;
+    }
+
+    /*!
+     * @param world            world coordinates
+     * @param transformation   transformation to apply to the given world coordinates, if any
+     */
+    template<glm::length_t dimensions, typename Type, glm::qualifier qualifier>
+    glm::vec2 world_to_viewport(const glm::vec<dimensions, Type, qualifier>& world, const glm::vec2& viewport, const glm::mat4& transformation = glm::mat4{1.0f})
+    {
+        glm::vec3 ndc = world_to_ndc(world, transformation);
+        return (glm::vec2{ndc.x, ndc.y} + 1.0f) / 2.0f * viewport;
+    }
 }