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%% This is an example. Feel free to copy and reuse as you wish.
-module(matrix3d).
-export([rotate_x/1, rotate_y/1, rotate_z/1, multiply/2, apply/2]).
% Rotation matrix around X-axis (angle in radians)
rotate_x(Angle) ->
Cos = math:cos(Angle),
Sin = math:sin(Angle),
[[1, 0, 0 ],
[0, Cos, -Sin ],
[0, Sin, Cos]].
% Rotation matrix around Y-axis
rotate_y(Angle) ->
Cos = math:cos(Angle),
Sin = math:sin(Angle),
[[ Cos, 0, Sin ],
[ 0, 1, 0 ],
[-Sin, 0, Cos]].
% Rotation matrix around Z-axis
rotate_z(Angle) ->
Cos = math:cos(Angle),
Sin = math:sin(Angle),
[[Cos, -Sin, 0 ],
[Sin, Cos, 0 ],
[0, 0, 1]].
% Multiply two 3x3 matrices
multiply(A, B) ->
[[A11, A12, A13],
[A21, A22, A23],
[A31, A32, A33]] = A,
[[B11, B12, B13],
[B21, B22, B23],
[B31, B32, B33]] = B,
[[A11*B11 + A12*B21 + A13*B31, A11*B12 + A12*B22 + A13*B32, A11*B13 + A12*B23 + A13*B33],
[A21*B11 + A22*B21 + A23*B31, A21*B12 + A22*B22 + A23*B32, A21*B13 + A22*B23 + A23*B33],
[A31*B11 + A32*B21 + A33*B31, A31*B12 + A32*B22 + A33*B32, A31*B13 + A32*B23 + A33*B33]].
% Apply a 3x3 matrix to a 3D vertex {X, Y, Z}
apply(Matrix, {X, Y, Z}) ->
[[M11, M12, M13],
[M21, M22, M23],
[M31, M32, M33]] = Matrix,
NewX = M11 * X + M12 * Y + M13 * Z,
NewY = M21 * X + M22 * Y + M23 * Z,
NewZ = M31 * X + M32 * Y + M33 * Z,
{NewX, NewY, NewZ}.
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