code

scripts/cube_logic.lua

@@ -35,6 +35,8 @@ local pyramid_indices = {
     4, 5, 2,
 }
 
+local math3d = require("math3d")
+
 local rotation_speeds = {x = 0.5, y = 0.7}
 
 local shader_variants = {
@@ -52,62 +54,26 @@ local shader_variants = {
     },
 }
 
-local function rotation_y(radians)
-    local c = math.cos(radians)
-    local s = math.sin(radians)
-    return {
-        c,  0.0, -s, 0.0,
-        0.0, 1.0, 0.0, 0.0,
-        s,  0.0,  c, 0.0,
-        0.0, 0.0, 0.0, 1.0,
-    }
-end
-
-local function rotation_x(radians)
-    local c = math.cos(radians)
-    local s = math.sin(radians)
-    return {
-        1.0, 0.0, 0.0, 0.0,
-        0.0,  c,  s, 0.0,
-        0.0, -s,  c, 0.0,
-        0.0, 0.0, 0.0, 1.0,
-    }
-end
-
-local function multiply_matrices(a, b)
-    local result = {}
-    for row = 1, 4 do
-        for col = 1, 4 do
-            local sum = 0.0
-            for idx = 1, 4 do
-                sum = sum + a[(idx - 1) * 4 + row] * b[(col - 1) * 4 + idx]
-            end
-            result[(col - 1) * 4 + row] = sum
-        end
-    end
-    return result
-end
-
-local function translation(x, y, z)
-    return {
-        1.0, 0.0, 0.0, 0.0,
-        0.0, 1.0, 0.0, 0.0,
-        0.0, 0.0, 1.0, 0.0,
-        x,   y,   z,   1.0,
-    }
-end
+local camera = {
+    eye = {2.0, 2.0, 2.5},
+    center = {0.0, 0.0, 0.0},
+    up = {0.0, 1.0, 0.0},
+    fov = 0.78,
+    near = 0.1,
+    far = 10.0,
+}
 
 local function build_model(time)
-    local y = rotation_y(time * rotation_speeds.y)
-    local x = rotation_x(time * rotation_speeds.x)
-    return multiply_matrices(y, x)
+    local y = math3d.rotation_y(time * rotation_speeds.y)
+    local x = math3d.rotation_x(time * rotation_speeds.x)
+    return math3d.multiply(y, x)
 end
 
 local function create_cube(position, speed_scale, shader_key)
     local function compute_model_matrix(time)
         local base = build_model(time * speed_scale)
-        local offset = translation(position[1], position[2], position[3])
-        return multiply_matrices(offset, base)
+        local offset = math3d.translation(position[1], position[2], position[3])
+        return math3d.multiply(offset, base)
     end
 
     return {
@@ -121,8 +87,8 @@ end
 local function create_pyramid(position, shader_key)
     local function compute_model_matrix(time)
         local base = build_model(time * 0.6)
-        local offset = translation(position[1], position[2], position[3])
-        return multiply_matrices(offset, base)
+        local offset = math3d.translation(position[1], position[2], position[3])
+        return math3d.multiply(offset, base)
     end
 
     return {
@@ -145,3 +111,9 @@ end
 function get_shader_paths()
     return shader_variants
 end
+
+function get_view_projection(aspect)
+    local view = math3d.look_at(camera.eye, camera.center, camera.up)
+    local projection = math3d.perspective(camera.fov, aspect, camera.near, camera.far)
+    return math3d.multiply(projection, view)
+end

scripts/math3d.lua

@@ -0,0 +1,119 @@
+local math3d = {}
+
+local function normalize(vec)
+    local x, y, z = vec[1], vec[2], vec[3]
+    local len = math.sqrt(x * x + y * y + z * z)
+    if len == 0.0 then
+        return {x, y, z}
+    end
+    return {x / len, y / len, z / len}
+end
+
+local function cross(a, b)
+    return {
+        a[2] * b[3] - a[3] * b[2],
+        a[3] * b[1] - a[1] * b[3],
+        a[1] * b[2] - a[2] * b[1],
+    }
+end
+
+local function dot(a, b)
+    return a[1] * b[1] + a[2] * b[2] + a[3] * b[3]
+end
+
+local function identity_matrix()
+    return {
+        1.0, 0.0, 0.0, 0.0,
+        0.0, 1.0, 0.0, 0.0,
+        0.0, 0.0, 1.0, 0.0,
+        0.0, 0.0, 0.0, 1.0,
+    }
+end
+
+function math3d.identity()
+    return identity_matrix()
+end
+
+function math3d.multiply(a, b)
+    local result = {}
+    for row = 1, 4 do
+        for col = 1, 4 do
+            local sum = 0.0
+            for idx = 1, 4 do
+                sum = sum + a[(idx - 1) * 4 + row] * b[(col - 1) * 4 + idx]
+            end
+            result[(col - 1) * 4 + row] = sum
+        end
+    end
+    return result
+end
+
+function math3d.translation(x, y, z)
+    return {
+        1.0, 0.0, 0.0, 0.0,
+        0.0, 1.0, 0.0, 0.0,
+        0.0, 0.0, 1.0, 0.0,
+        x,   y,   z,   1.0,
+    }
+end
+
+function math3d.rotation_x(radians)
+    local c = math.cos(radians)
+    local s = math.sin(radians)
+    return {
+        1.0, 0.0, 0.0, 0.0,
+        0.0,  c,  s, 0.0,
+        0.0, -s,  c, 0.0,
+        0.0, 0.0, 0.0, 1.0,
+    }
+end
+
+function math3d.rotation_y(radians)
+    local c = math.cos(radians)
+    local s = math.sin(radians)
+    return {
+        c,  0.0, -s, 0.0,
+        0.0, 1.0, 0.0, 0.0,
+        s,  0.0,  c, 0.0,
+        0.0, 0.0, 0.0, 1.0,
+    }
+end
+
+function math3d.look_at(eye, center, up)
+    local f = normalize({center[1] - eye[1], center[2] - eye[2], center[3] - eye[3]})
+    local s = normalize(cross(f, up))
+    local u = cross(s, f)
+
+    local result = identity_matrix()
+    result[1] = s[1]
+    result[2] = u[1]
+    result[3] = -f[1]
+    result[5] = s[2]
+    result[6] = u[2]
+    result[7] = -f[2]
+    result[9] = s[3]
+    result[10] = u[3]
+    result[11] = -f[3]
+    result[13] = -dot(s, eye)
+    result[14] = -dot(u, eye)
+    result[15] = dot(f, eye)
+    return result
+end
+
+function math3d.perspective(fov, aspect, zNear, zFar)
+    local tanHalf = math.tan(fov / 2.0)
+    local result = {
+        0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0,
+    }
+    result[1] = 1.0 / (aspect * tanHalf)
+    result[6] = -1.0 / tanHalf
+    result[11] = zFar / (zNear - zFar)
+    result[12] = -1.0
+    result[15] = (zNear * zFar) / (zNear - zFar)
+    return result
+end
+
+return math3d