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Merge pull request #175 from EmperorArthur/affine_hell
Use Affine Transformation Matrices For sweep_rounded
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Ruud
GitHub
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36345f3efb
2 changed files with 170 additions and 57 deletions
169
generic-helpers.scad
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169
generic-helpers.scad
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/**
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* @file generic-helpers.scad
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* @brief Generic Helper Functions. Not gridfinity specific.
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*/
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function clp(x,a,b) = min(max(x,a),b);
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module rounded_rectangle(length, width, height, rad) {
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linear_extrude(height)
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offset(rad)
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offset(-rad)
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square([length,width], center = true);
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}
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module rounded_square(length, height, rad) {
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rounded_rectangle(length, length, height, rad);
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}
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module copy_mirror(vec=[0,1,0]) {
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children();
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if (vec != [0,0,0])
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mirror(vec)
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children();
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}
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module pattern_linear(x = 1, y = 1, sx = 0, sy = 0) {
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yy = sy <= 0 ? sx : sy;
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translate([-(x-1)*sx/2,-(y-1)*yy/2,0])
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for (i = [1:ceil(x)])
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for (j = [1:ceil(y)])
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translate([(i-1)*sx,(j-1)*yy,0])
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children();
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}
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module pattern_circular(n=2) {
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for (i = [1:n])
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rotate(i*360/n)
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children();
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}
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/**
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* @brief Unity (no change) affine transformation matrix.
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* @details For use with multmatrix transforms.
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*/
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unity_matrix = [
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[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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];
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/**
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* @brief Get the magnitude of a 2d or 3d vector
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* @param vector A 2d or 3d vectorm
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* @returns Magnitude of the vector.
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*/
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function vector_magnitude(vector) =
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sqrt(vector.x^2 + vector.y^2 + (len(vector) == 3 ? vector.z^2 : 0));
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/**
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* @brief Convert a 2d or 3d vector into a unit vector
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* @returns The unit vector. Where total magnitude is 1.
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*/
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function vector_as_unit(vector) = vector / vector_magnitude(vector);
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/**
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* @brief Convert a 2d vector into an angle.
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* @details Just a wrapper around atan2.
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* @param A 2d vectorm
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* @returns Angle of the vector.
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*/
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function atanv(vector) = atan2(vector.y, vector.x);
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function _affine_rotate_x(angle_x) = [
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[1, 0, 0, 0],
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[0, cos(angle_x), -sin(angle_x), 0],
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[0, sin(angle_x), cos(angle_x), 0],
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[0, 0, 0, 1]
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];
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function _affine_rotate_y(angle_y) = [
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[cos(angle_y), 0, sin(angle_y), 0],
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[0, 1, 0, 0],
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[-sin(angle_y), 0, cos(angle_y), 0],
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[0, 0, 0, 1]
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];
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function _affine_rotate_z(angle_z) = [
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[cos(angle_z), -sin(angle_z), 0, 0],
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[sin(angle_z), cos(angle_z), 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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];
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/**
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* @brief Affine transformation matrix equivalent of `rotate`
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* @param angle_vector @see `rotate`
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* @details Equivalent to `rotate([0, angle, 0])`
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* @returns An affine transformation matrix for use with `multmatrix()`
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*/
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function affine_rotate(angle_vector) =
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_affine_rotate_z(angle_vector.z) * _affine_rotate_y(angle_vector.y) * _affine_rotate_x(angle_vector.x);
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/**
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* @brief Affine transformation matrix equivalent of `translate`
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* @param vector @see `translate`
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* @returns An affine transformation matrix for use with `multmatrix()`
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*/
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function affine_translate(vector) = [
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[1, 0, 0, vector.x],
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[0, 1, 0, vector.y],
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[0, 0, 1, vector.z],
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[0, 0, 0, 1]
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];
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/**
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* @brief Create a rectangle with rounded corners by sweeping a 2d object along a path.
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* Centered on origin.
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*/
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module sweep_rounded(width=10, length=10) {
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half_width = width/2;
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half_length = length/2;
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path_points = [
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[-half_width, half_length], //Start
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[half_width, half_length], // Over
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[half_width, -half_length], //Down
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[-half_width, -half_length], // Back over
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[-half_width, half_length] // Up to start
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];
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path_vectors = [
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path_points[1] - path_points[0],
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path_points[2] - path_points[1],
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path_points[3] - path_points[2],
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path_points[4] - path_points[3],
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];
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// These contain the translations, but not the rotations
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// OpenSCAD requires this hacky for loop to get accumulate to work!
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first_translation = affine_translate([path_points[0].y, 0,path_points[0].x]);
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affine_translations = concat([first_translation], [
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for (i = 0, a = first_translation;
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i < len(path_vectors);
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a=a * affine_translate([path_vectors[i].y, 0, path_vectors[i].x]), i=i+1)
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a * affine_translate([path_vectors[i].y, 0, path_vectors[i].x])
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]);
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// Bring extrusion to the xy plane
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affine_matrix = affine_rotate([90, 0, 90]);
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walls = [
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for (i = [0 : len(path_vectors) - 1])
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affine_matrix * affine_translations[i]
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* affine_rotate([0, atanv(path_vectors[i]), 0])
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];
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union()
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{
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for (i = [0 : len(walls) - 1]){
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multmatrix(walls[i])
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linear_extrude(vector_magnitude(path_vectors[i]))
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children();
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// Rounded Corners
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multmatrix(walls[i] * affine_rotate([-90, 0, 0]))
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rotate_extrude(angle = 90, convexity = 4)
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children();
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}
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}
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}
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@ -5,6 +5,7 @@
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*/
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include <standard.scad>
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use <generic-helpers.scad>
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// ===== User Modules ===== //
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@ -623,60 +624,3 @@ module profile_cutter_tab(h, tab, ang) {
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polygon([[0,h],[tab,h],[0,h-tab*tan(ang)]]);
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}
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// ==== Utilities =====
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function clp(x,a,b) = min(max(x,a),b);
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module rounded_rectangle(length, width, height, rad) {
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linear_extrude(height)
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offset(rad)
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offset(-rad)
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square([length,width], center = true);
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}
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module rounded_square(length, height, rad) {
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rounded_rectangle(length, length, height, rad);
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}
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module copy_mirror(vec=[0,1,0]) {
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children();
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if (vec != [0,0,0])
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mirror(vec)
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children();
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}
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module pattern_linear(x = 1, y = 1, sx = 0, sy = 0) {
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yy = sy <= 0 ? sx : sy;
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translate([-(x-1)*sx/2,-(y-1)*yy/2,0])
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for (i = [1:ceil(x)])
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for (j = [1:ceil(y)])
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translate([(i-1)*sx,(j-1)*yy,0])
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children();
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}
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module pattern_circular(n=2) {
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for (i = [1:n])
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rotate(i*360/n)
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children();
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}
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module sweep_rounded(w=10, h=10) {
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union() pattern_circular(2) {
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copy_mirror([1,0,0])
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translate([w/2,h/2,0])
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rotate_extrude(angle = 90, convexity = 4)
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children();
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translate([w/2,0,0])
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rotate([90,0,0])
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linear_extrude(height = h, center = true)
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children();
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rotate([0,0,90])
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translate([h/2,0,0])
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rotate([90,0,0])
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linear_extrude(height = w, center = true)
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children();
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}
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}
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