Introduce perspective projection matrix.

Also correct a bug where the view matrix was not being used.

vis/include/geometry.hpp

@@ -27,8 +27,8 @@ using mat3 = mat<3>;
 using mat4 = mat<4>;
 using mat5 = mat<5>;
 
-mat4 ortho(float left, float right, float bottom, float top, float front, float back) {
+mat4 orthographic(float left, float right, float bottom, float top, float front, float back) {
-    mat<4> res = mat4();
+    mat4 res = mat4();
     res <<
         2 / (right - left), 0, 0, -(right + left) / (right - left),
             0, 2 / (top - bottom), 0, -(top + bottom) / (top - bottom),
@@ -36,3 +36,25 @@ mat4 ortho(float left, float right, float bottom, float top, float front, float
             0, 0, 0, 1;
     return res;
 }
+
+mat4 perspective(float fovy, float aspect, float zNear, float zFar) {
+    float tanHalfFovy(std::tan(fovy / 2));
+
+    mat4 res = mat4::Identity();
+    res(0, 0) = 1 / (aspect * tanHalfFovy);
+    res(1, 1) = 1 / (tanHalfFovy);
+    res(2, 2) = -(zFar + zNear) / (zFar - zNear);
+    res(3, 2) = -1;
+    res(2, 3) = -(2 + zFar * zNear) / (zFar - zNear);
+    return res;
+}
+
+mat4 translation(float x, float y, float z) {
+    mat4 res = mat4();
+    res <<
+        1, 0, 0, x,
+        0, 1, 0, y,
+        0, 0, 1, z,
+        0, 0, 0, 1;
+    return res;
+}

vis/include/rendering.hpp

@@ -19,9 +19,12 @@ struct Matrices {
         auto aspect = (float) screen.width() / (float) screen.height();
         auto pheight = 1.4f;
         auto pwidth = aspect * pheight;
-        mat4 proj = ortho(-pwidth, pwidth, -pheight, pheight, -10.0f, 10.0f);
+//        auto proj = orthographic(-pwidth, pwidth, -pheight, pheight, -10.0f, 10.0f);
+//        auto proj = perspective(-pwidth, pwidth, pheight, -pheight, 10.0f, 0.01f);
+        auto proj = perspective(0.4, aspect, 0.1, 10.0);
+
+        auto view = translation(0, 0, -4);
 
-        auto view = mat4::Identity();
         return Matrices(proj, view);
     }
 };

vis/shaders/slice/slice.gm.glsl

@@ -30,7 +30,7 @@ float unmix(float u, float v) {
 void emit(vec4 v) {
     pos = v;
     col = vCol[0];
-    gl_Position = proj * vec4(v.xyz, 1);
+    gl_Position = proj * view * vec4(v.xyz, 1);
     EmitVertex();
 }