| // |matrix| - Float32Array, |input| - point-like dict (must have x, y, z, w) |
| let transform_point_by_matrix = function(matrix, input) { |
| return { |
| x : matrix[0] * input.x + matrix[4] * input.y + matrix[8] * input.z + matrix[12] * input.w, |
| y : matrix[1] * input.x + matrix[5] * input.y + matrix[9] * input.z + matrix[13] * input.w, |
| z : matrix[2] * input.x + matrix[6] * input.y + matrix[10] * input.z + matrix[14] * input.w, |
| w : matrix[3] * input.x + matrix[7] * input.y + matrix[11] * input.z + matrix[15] * input.w, |
| }; |
| } |
| |
| // Creates a unit-length quaternion. |
| // |input| - point-like dict (must have x, y, z, w) |
| let normalize_quaternion = function(input) { |
| const length_squared = input.x * input.x + input.y * input.y + input.z * input.z + input.w * input.w; |
| const length = Math.sqrt(length_squared); |
| |
| return {x : input.x / length, y : input.y / length, z : input.z / length, w : input.w / length}; |
| } |
| |
| // Returns negated quaternion. |
| // |input| - point-like dict (must have x, y, z, w) |
| let flip_quaternion = function(input) { |
| return {x : -input.x, y : -input.y, z : -input.z, w : -input.w}; |
| } |
| |
| // |input| - point-like dict (must have x, y, z, w) |
| let conjugate_quaternion = function(input) { |
| return {x : -input.x, y : -input.y, z : -input.z, w : input.w}; |
| } |
| |
| let multiply_quaternions = function(q1, q2) { |
| return { |
| w : q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z, |
| x : q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y, |
| y : q1.w * q2.y - q1.x * q2.z + q1.y * q2.w + q1.z * q2.x, |
| z : q1.w * q2.z + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w, |
| } |
| } |
| |
| // |point| - point-like dict (must have x, y, z, w) |
| let normalize_perspective = function(point) { |
| if(point.w == 0 || point.w == 1) return point; |
| |
| return { |
| x : point.x / point.w, |
| y : point.y / point.w, |
| z : point.z / point.w, |
| w : 1 |
| }; |
| } |
| |
| // |quaternion| - point-like dict (must have x, y, z, w), |
| // |input| - point-like dict (must have x, y, z, w) |
| let transform_point_by_quaternion = function(quaternion, input) { |
| const q_normalized = normalize_quaternion(quaternion); |
| const q_conj = conjugate_quaternion(q_normalized); |
| const p_in = normalize_perspective(input); |
| |
| // construct a quaternion out of the point (take xyz & zero the real part). |
| const p = {x : p_in.x, y : p_in.y, z : p_in.z, w : 0}; |
| |
| // transform the input point |
| const p_mul = multiply_quaternions( q_normalized, multiply_quaternions(p, q_conj) ); |
| |
| // add back the w component of the input |
| return { x : p_mul.x, y : p_mul.y, z : p_mul.z, w : p_in.w }; |
| } |