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Use Affine transformation matrices for creating walls.

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This involves more math, but results in a cleaner abstract syntax tree.
Which also means it is cleaner when importing to something like FreeCAD.
This commit is contained in:
Arthur Moore 2024-02-24 18:04:18 -05:00
parent 015daff2e8
commit 1cf350121d
1 changed files with 126 additions and 15 deletions
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141
gridfinity-rebuilt-utility.scad
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@ -659,22 +659,133 @@ module pattern_circular(n=2) {
children();
}
module sweep_rounded(w=10, h=10) {
union() pattern_circular(2) {
copy_mirror([1,0,0])
translate([w/2,h/2,0])
/**
* @brief Unity (no change) affine transformation matrix.
* @details For use with multmatrix transforms.
*/
unity_matrix = [
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]
];
/**
* @brief Get the magnitude of a 2d or 3d vector
* @param vector A 2d or 3d vectorm
* @returns Magnitude of the vector.
*/
function vector_magnitude(vector) =
sqrt(vector.x^2 + vector.y^2 + (len(vector) == 3 ? vector.z^2 : 0));
/**
* @brief Convert a 2d or 3d vector into a unit vector
* @returns The unit vector. Where total magnitude is 1.
*/
function vector_as_unit(vector) = vector / vector_magnitude(vector);
/**
* @brief Convert a 2d vector into an angle.
* @details Just a wrapper around atan2.
* @param A 2d vectorm
* @returns Angle of the vector.
*/
function atanv(vector) = atan2(vector.y, vector.x);
/**
* @brief Affine transformation matrix for 2d rotation on the X,Y plane.
* @param angle The angle to rotate things by
* @returns an Affine transformation matrix for use with `multmatrix()`
*/
function affine_rotation(angle) = [
[cos(angle), 0, sin(angle), 0],
[0, 1, 0, 0],
[-sin(angle), 0, cos(angle), 0],
[0, 0, 0, 1]
];
/**
* @brief Affine transformation matrix for 2d translation on the X,Y plane.
* @param vector 2d Vector to translate by.
* @returns an Affine transformation matrix for use with `multmatrix()`
*/
function affine_translation(vector) = [
[1, 0, 0, vector.y],
[0, 1, 0, 0],
[0, 0, 1, vector.x],
[0, 0, 0, 1]
];
/**
* @brief Create a rectangle with rounded corners by sweeping a 2d object along a path.
* Centered on origin.
*/
module sweep_rounded(width=10, length=10) {
half_width = width/2;
half_length = length/2;
path_points = [
[-half_width, half_length], //Start
[half_width, half_length], // Over
[half_width, -half_length], //Down
[-half_width, -half_length], // Back over
[-half_width, half_length] // Up to start
];
path_vectors = [
path_points[1] - path_points[0],
path_points[2] - path_points[1],
path_points[3] - path_points[2],
path_points[4] - path_points[3],
];
// These contain the translations, but not the rotations
// OpenSCAD requires this hacky for loop to get accumulate to work!
first_translation = affine_translation(path_points[0]);
affine_translations = concat([first_translation], [
for (i = 0, a = first_translation;
i < len(path_vectors);
a=a * affine_translation(path_vectors[i]), i=i+1)
a * affine_translation(path_vectors[i])
]);
// Affine matrix to rotate around X axis
rot_x = 90;
x_matrix = [
[1, 0, 0, 0],
[0, cos(rot_x), -sin(rot_x), 0],
[0, sin(rot_x), cos(rot_x), 0],
[0, 0, 0, 1]
];
// Affine matrix to rotate around Z axis
z_rot = 90;
z_matrix = [
[cos(z_rot), -sin(z_rot), 0, 0],
[sin(z_rot), cos(z_rot), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]
];
// Bring extrusion to the xy plane
affine_matrix = z_matrix * x_matrix;
walls = [
for (i = [0 : len(path_vectors) - 1])
affine_matrix * affine_translations[i]
* affine_rotation(atanv(path_vectors[i]))
];
union()
{
for (i = [0 : len(walls) - 1]){
multmatrix(walls[i])
linear_extrude(vector_magnitude(path_vectors[i]))
children();
// Rounded Corners
multmatrix(walls[i]
*x_matrix*x_matrix*x_matrix *z_matrix*z_matrix*z_matrix*z_matrix)
rotate_extrude(angle = 90, convexity = 4)
children();
translate([w/2,0,0])
rotate([90,0,0])
linear_extrude(height = h, center = true)
children();
rotate([0,0,90])
translate([h/2,0,0])
rotate([90,0,0])
linear_extrude(height = w, center = true)
children();
}
}
}