code

scripts/math3d.lua

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+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