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Added functions to translate, scale, and rotate arrays of 3d points.

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Revar Desmera 2018-11-25 12:49:44 -08:00
parent 34dc5ed72e
commit 81210a2a95
1 changed files with 37 additions and 3 deletions
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math.scad
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@ -177,7 +177,9 @@ function matrix4_zrot(ang) = mat3_to_mat4(matrix3_zrot(ang));
// u = axis vector to rotate around.
// ang = number of degrees to rotate.
function matrix3_rot_by_axis(u, ang) = let(
c = cos(ang), c2 = 1-c, s = sin(ang)
u = normalize(u),
c = cos(ang),
c2 = 1-c, s = sin(ang)
) [
[u[0]*u[0]*c2+c, u[0]*u[1]*c2-u[2]*s, u[0]*u[2]*c2+u[1]*s],
[u[1]*u[0]*c2+u[2]*s, u[1]*u[1]*c2+c, u[1]*u[2]*c2-u[0]*s],
@ -191,6 +193,32 @@ function matrix3_rot_by_axis(u, ang) = let(
function matrix4_rot_by_axis(u, ang) = mat3_to_mat4(matrix3_rot_by_axis(u, ang));
// moves each point in an array by a given amount.
function translate_points(pts, v=[0,0,0]) = [for (pt = pts) pt+v];
// Scales each point in an array by a given amount, around a given centerpoint.
function scale_points(pts, v=[0,0,0], cp=[0,0,0]) = [for (pt = pts) [for (i = [0:len(pt)-1]) (pt[i]-cp[i])*v[i]+cp[i]]];
// Rotates each 2D point in an array by a given amount, around a given centerpoint.
function rotate_points2d(pts, ang, cp=[0,0]) = let(
m = matrix3_zrot(ang)
) [for (pt = pts) m*point3d(pt-cp)+cp];
// Rotates each 3D point in an array by a given amount, around a given centerpoint.
function rotate_points3d(pts, v=[0,0,0], cp=[0,0,0]) = let(
m = matrix4_zrot(v[2]) * matrix4_yrot(v[1]) * matrix4_xrot(v[0])
) [for (pt = pts) m*concat(point3d(pt)-cp, 0)+cp];
// Rotates each 3D point in an array by a given amount, around a given centerpoint and axis.
function rotate_points3d_around_axis(pts, ang, u=[0,0,0], cp=[0,0,0]) = let(
m = matrix4_rot_by_axis(u, ang)
) [for (pt = pts) m*concat(point3d(pt)-cp, 0)+cp];
// Gives the sum of a series of sines, at a given angle.
// a = angle to get the value for.
// sines = array of [amplitude, frequency] pairs, where the frequency is the
@ -200,6 +228,12 @@ function sum_of_sines(a,sines) = len(sines)==0? 0 :
sum_of_sines(a,[sines[0]])+sum_of_sines(a,cdr(sines));
// Constrains value to a range of values between minval and maxval, inclusive.
// v = value to constrain.
// minval = minimum value to return, if out of range.
// maxval = maximum value to return, if out of range.
function constrain(v, minval, maxval) = min(maxval, max(minval, v));
// Returns unit length normalized version of vector v.
function normalize(v) = v/norm(v);
@ -207,8 +241,8 @@ function normalize(v) = v/norm(v);
function vector2d_angle(v1,v2) = atan2(v1[1],v1[0]) - atan2(v2[1],v2[0]);
// Returns angle in degrees between two 3D vectors.
// NOTE: min and max are to correct for crazy FP rounding errors that exceed acos()'s domain.
function vector3d_angle(v1,v2) = acos(max(-1,min(1,(v1*v2)/(norm(v1)*norm(v2)))));
// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
function vector3d_angle(v1,v2) = acos(constrain((v1*v2)/(norm(v1)*norm(v2)), -1, 1));
// Returns a slice of an array. An index of 0 is the array start, -1 is array end
function slice(arr,st,end) = let(