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Enabled coordinate translations of lists of coords.

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Revar Desmera 2023-05-14 03:17:41 -07:00
parent 1e05cdbd15
commit e210ff1fdd
1 changed files with 114 additions and 50 deletions
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@ -136,13 +136,16 @@ function path4d(points, fill=0) =
// Function: polar_to_xy() // Function: polar_to_xy()
// Usage: // Usage:
// pt = polar_to_xy(r, theta); // pt = polar_to_xy(r, theta);
// pt = polar_to_xy([r, theta]); // pt = polar_to_xy([R, THETA]);
// pts = polar_to_xy([[R,THETA], [R,THETA], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// Synopsis: Convert 2d polar coordinates to cartesian coordinates. // Synopsis: Convert 2d polar coordinates to cartesian coordinates.
// See Also: xy_to_polar(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz() // See Also: xy_to_polar(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Description: // Description:
// Convert polar coordinates to 2D cartesian coordinates. // Called with two arguments, converts the `r` and `theta` 2D polar coordinate into an `[X,Y]` cartesian coordinate.
// Returns [X,Y] cartesian coordinates. // Called with one `[R,THETA]` vector argument, converts the 2D polar coordinate into an `[X,Y]` cartesian coordinate.
// Called with a list of `[R,THETA]` vector arguments, converts each 2D polar coordinate into `[X,Y]` cartesian coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane.
// Arguments: // Arguments:
// r = distance from the origin. // r = distance from the origin.
// theta = angle in degrees, counter-clockwise of X+. // theta = angle in degrees, counter-clockwise of X+.
@ -150,6 +153,7 @@ function path4d(points, fill=0) =
// xy = polar_to_xy(20,45); // Returns: ~[14.1421365, 14.1421365] // xy = polar_to_xy(20,45); // Returns: ~[14.1421365, 14.1421365]
// xy = polar_to_xy(40,30); // Returns: ~[34.6410162, 15] // xy = polar_to_xy(40,30); // Returns: ~[34.6410162, 15]
// xy = polar_to_xy([40,30]); // Returns: ~[34.6410162, 15] // xy = polar_to_xy([40,30]); // Returns: ~[34.6410162, 15]
// xy = polar_to_xy([[40,30],[20,120]]); // Returns: ~[[34.6410162, 15], [-10, 17.3205]]
// Example(2D): // Example(2D):
// r=40; ang=30; $fn=36; // r=40; ang=30; $fn=36;
// pt = polar_to_xy(r,ang); // pt = polar_to_xy(r,ang);
@ -157,28 +161,36 @@ function path4d(points, fill=0) =
// color("black") stroke([[r,0], [0,0], pt], width=0.5); // color("black") stroke([[r,0], [0,0], pt], width=0.5);
// color("black") stroke(arc(r=15, angle=ang), width=0.5); // color("black") stroke(arc(r=15, angle=ang), width=0.5);
// color("red") move(pt) circle(d=3); // color("red") move(pt) circle(d=3);
function polar_to_xy(r,theta=undef) = let( function polar_to_xy(r,theta) =
rad = theta==undef? r[0] : r, theta != undef
t = theta==undef? r[1] : theta ? assert(is_num(r) && is_num(theta), "Bad Arguments.")
) rad*[cos(t), sin(t)]; [r*cos(theta), r*sin(theta)]
: assert(is_list(r), "Bad Arguments")
is_num(r.x)
? polar_to_xy(r.x, r.y)
: [for(p = r) polar_to_xy(p.x, p.y)];
// Function: xy_to_polar() // Function: xy_to_polar()
// Usage: // Usage:
// r_theta = xy_to_polar(x,y); // r_theta = xy_to_polar(x,y);
// r_theta = xy_to_polar([X,Y]); // r_theta = xy_to_polar([X,Y]);
// r_thetas = xy_to_polar([[X,Y], [X,Y], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// Synopsis: Convert 2d cartesian coordinates to polar coordinates (radius and angle) // Synopsis: Convert 2d cartesian coordinates to polar coordinates (radius and angle)
// See Also: polar_to_xy(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz() // See Also: polar_to_xy(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Description: // Description:
// Convert 2D cartesian coordinates to polar coordinates. // Called with two arguments, converts the `x` and `y` 2D cartesian coordinate into a `[RADIUS,THETA]` polar coordinate.
// Returns [radius, theta] where theta is the angle counter-clockwise of X+. // Called with one `[X,Y]` vector argument, converts the 2D cartesian coordinate into a `[RADIUS,THETA]` polar coordinate.
// Called with a list of `[X,Y]` vector arguments, converts each 2D cartesian coordinate into `[RADIUS,THETA]` polar coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane.
// Arguments: // Arguments:
// x = X coordinate. // x = X coordinate.
// y = Y coordinate. // y = Y coordinate.
// Example: // Example:
// plr = xy_to_polar(20,30); // plr = xy_to_polar(20,30);
// plr = xy_to_polar([40,60]); // plr = xy_to_polar([40,60]);
// plrs = xy_to_polar([[40,60],[-10,20]]);
// Example(2D): // Example(2D):
// pt = [-20,30]; $fn = 36; // pt = [-20,30]; $fn = 36;
// rt = xy_to_polar(pt); // rt = xy_to_polar(pt);
@ -186,10 +198,14 @@ function polar_to_xy(r,theta=undef) = let(
// stroke(circle(r=r), closed=true, width=0.5); // stroke(circle(r=r), closed=true, width=0.5);
// zrot(ang) stroke([[0,0],[r,0]],width=0.5); // zrot(ang) stroke([[0,0],[r,0]],width=0.5);
// color("red") move(pt) circle(d=3); // color("red") move(pt) circle(d=3);
function xy_to_polar(x,y=undef) = let( function xy_to_polar(x, y) =
xx = y==undef? x[0] : x, y != undef
yy = y==undef? x[1] : y ? assert(is_num(x) && is_num(y), "Bad Arguments.")
) [norm([xx,yy]), atan2(yy,xx)]; [norm([x, y]), atan2(y, x)]
: assert(is_list(x), "Bad Arguments")
is_num(x.x)
? xy_to_polar(x.x, x.y)
: [for(p = x) xy_to_polar(p.x, p.y)];
// Function: project_plane() // Function: project_plane()
@ -324,12 +340,16 @@ function lift_plane(plane, p) =
// Function: cylindrical_to_xyz() // Function: cylindrical_to_xyz()
// Usage: // Usage:
// pt = cylindrical_to_xyz(r, theta, z); // pt = cylindrical_to_xyz(r, theta, z);
// pt = cylindrical_to_xyz([r, theta, z]); // pt = cylindrical_to_xyz([RADIUS,THETA,Z]);
// pts = cylindrical_to_xyz([[RADIUS,THETA,Z], [RADIUS,THETA,Z], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// See Also: xyz_to_cylindrical(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz() // See Also: xyz_to_cylindrical(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Synopsis: Convert cylindrical coordinates to cartesian coordinates. // Synopsis: Convert cylindrical coordinates to cartesian coordinates.
// Description: // Description:
// Convert cylindrical coordinates to 3D cartesian coordinates. Returns [X,Y,Z] cartesian coordinates. // Called with three arguments, converts the `r`, `theta`, and 'z' 3D cylindrical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with one `[RADIUS,THETA,Z]` vector argument, converts the 3D cylindrical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with a list of `[RADIUS,THETA,Z]` vector arguments, converts each 3D cylindrical coordinate into `[X,Y,Z]` cartesian coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane. Z is height above the XY plane.
// Arguments: // Arguments:
// r = distance from the Z axis. // r = distance from the Z axis.
// theta = angle in degrees, counter-clockwise of X+ on the XY plane. // theta = angle in degrees, counter-clockwise of X+ on the XY plane.
@ -337,22 +357,28 @@ function lift_plane(plane, p) =
// Example: // Example:
// xyz = cylindrical_to_xyz(20,30,40); // xyz = cylindrical_to_xyz(20,30,40);
// xyz = cylindrical_to_xyz([40,60,50]); // xyz = cylindrical_to_xyz([40,60,50]);
function cylindrical_to_xyz(r,theta=undef,z=undef) = let( function cylindrical_to_xyz(r,theta,z) =
rad = theta==undef? r[0] : r, theta != undef
t = theta==undef? r[1] : theta, ? assert(is_num(r) && is_num(theta) && is_num(z), "Bad Arguments.")
zed = theta==undef? r[2] : z [r*cos(theta), r*sin(theta), z]
) [rad*cos(t), rad*sin(t), zed]; : assert(is_list(r), "Bad Arguments")
is_num(r.x)
? cylindrical_to_xyz(r.x, r.y, r.z)
: [for(p = r) cylindrical_to_xyz(p.x, p.y, p.z)];
// Function: xyz_to_cylindrical() // Function: xyz_to_cylindrical()
// Usage: // Usage:
// rtz = xyz_to_cylindrical(x,y,z); // rtz = xyz_to_cylindrical(x,y,z);
// rtz = xyz_to_cylindrical([X,Y,Z]); // rtz = xyz_to_cylindrical([X,Y,Z]);
// rtzs = xyz_to_cylindrical([[X,Y,Z], [X,Y,Z], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// Synopsis: Convert 3d cartesian coordinates to cylindrical coordinates. // Synopsis: Convert 3d cartesian coordinates to cylindrical coordinates.
// See Also: cylindrical_to_xyz(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz() // See Also: cylindrical_to_xyz(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Description: // Description:
// Convert 3D cartesian coordinates to cylindrical coordinates. Returns [radius,theta,Z]. // Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into a `[RADIUS,THETA,Z]` cylindrical coordinate.
// Called with one `[X,Y,Z]` vector argument, converts the 3D cartesian coordinate into a `[RADIUS,THETA,Z]` cylindrical coordinate.
// Called with a list of `[X,Y,Z]` vector arguments, converts each 3D cartesian coordinate into `[RADIUS,THETA,Z]` cylindrical coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane. Z is height above the XY plane. // Theta is the angle counter-clockwise of X+ on the XY plane. Z is height above the XY plane.
// Arguments: // Arguments:
// x = X coordinate. // x = X coordinate.
@ -361,17 +387,27 @@ function cylindrical_to_xyz(r,theta=undef,z=undef) = let(
// Example: // Example:
// cyl = xyz_to_cylindrical(20,30,40); // cyl = xyz_to_cylindrical(20,30,40);
// cyl = xyz_to_cylindrical([40,50,70]); // cyl = xyz_to_cylindrical([40,50,70]);
function xyz_to_cylindrical(x,y=undef,z=undef) = let( // cyls = xyz_to_cylindrical([[40,50,70], [-10,15,-30]]);
p = is_num(x)? [x, default(y,0), default(z,0)] : point3d(x) function xyz_to_cylindrical(x,y,z) =
) [norm([p.x,p.y]), atan2(p.y,p.x), p.z]; y != undef
? assert(is_num(x) && is_num(y) && is_num(z), "Bad Arguments.")
[norm([x,y]), atan2(y,x), z]
: assert(is_list(x), "Bad Arguments")
is_num(x.x)
? xyz_to_cylindrical(x.x, x.y, x.z)
: [for(p = x) xyz_to_cylindrical(p.x, p.y, p.z)];
// Function: spherical_to_xyz() // Function: spherical_to_xyz()
// Usage: // Usage:
// pt = spherical_to_xyz(r, theta, phi); // pt = spherical_to_xyz(r, theta, phi);
// pt = spherical_to_xyz([r, theta, phi]); // pt = spherical_to_xyz([RADIUS,THETA,PHI]);
// pts = spherical_to_xyz([[RADIUS,THETA,PHI], [RADIUS,THETA,PHI], ...]);
// Description: // Description:
// Convert spherical coordinates to 3D cartesian coordinates. Returns [X,Y,Z] cartesian coordinates. // Called with three arguments, converts the `r`, `theta`, and 'phi' 3D spherical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with one `[RADIUS,THETA,PHI]` vector argument, converts the 3D spherical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with a list of `[RADIUS,THETA,PHI]` vector arguments, converts each 3D spherical coordinate into `[X,Y,Z]` cartesian coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane. Phi is the angle down from the Z+ pole.
// Synopsis: Convert spherical coordinates to 3d cartesian coordinates. // Synopsis: Convert spherical coordinates to 3d cartesian coordinates.
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz() // See Also: cylindrical_to_xyz(), xyz_to_spherical(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz()
@ -382,23 +418,30 @@ function xyz_to_cylindrical(x,y=undef,z=undef) = let(
// Example: // Example:
// xyz = spherical_to_xyz(20,30,40); // xyz = spherical_to_xyz(20,30,40);
// xyz = spherical_to_xyz([40,60,50]); // xyz = spherical_to_xyz([40,60,50]);
function spherical_to_xyz(r,theta=undef,phi=undef) = let( // xyzs = spherical_to_xyz([[40,60,50], [50,120,100]]);
rad = theta==undef? r[0] : r, function spherical_to_xyz(r,theta,phi) =
t = theta==undef? r[1] : theta, theta != undef
p = theta==undef? r[2] : phi ? assert(is_num(r) && is_num(theta) && is_num(phi), "Bad Arguments.")
) rad*[sin(p)*cos(t), sin(p)*sin(t), cos(p)]; r*[cos(theta)*sin(phi), sin(theta)*sin(phi), cos(phi)]
: assert(is_list(r), "Bad Arguments")
is_num(r.x)
? spherical_to_xyz(r.x, r.y, r.z)
: [for(p = r) spherical_to_xyz(p.x, p.y, p.z)];
// Function: xyz_to_spherical() // Function: xyz_to_spherical()
// Usage: // Usage:
// r_theta_phi = xyz_to_spherical(x,y,z) // r_theta_phi = xyz_to_spherical(x,y,z)
// r_theta_phi = xyz_to_spherical([X,Y,Z]) // r_theta_phi = xyz_to_spherical([X,Y,Z])
// r_theta_phis = xyz_to_spherical([[X,Y,Z], [X,Y,Z], ...])
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// Synopsis: Convert 3d cartesian coordinates to spherical coordinates. // Synopsis: Convert 3d cartesian coordinates to spherical coordinates.
// See Also: cylindrical_to_xyz(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz() // See Also: cylindrical_to_xyz(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz()
// Description: // Description:
// Convert 3D cartesian coordinates to spherical coordinates. Returns [r,theta,phi], where phi is // Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into a `[RADIUS,THETA,PHI]` spherical coordinate.
// the angle from the Z+ pole, and theta is degrees counter-clockwise of X+ on the XY plane. // Called with one `[X,Y,Z]` vector argument, converts the 3D cartesian coordinate into a `[RADIUS,THETA,PHI]` spherical coordinate.
// Called with a list of `[X,Y,Z]` vector arguments, converts each 3D cartesian coordinate into `[RADIUS,THETA,PHI]` spherical coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane. Phi is the angle down from the Z+ pole.
// Arguments: // Arguments:
// x = X coordinate. // x = X coordinate.
// y = Y coordinate. // y = Y coordinate.
@ -406,21 +449,31 @@ function spherical_to_xyz(r,theta=undef,phi=undef) = let(
// Example: // Example:
// sph = xyz_to_spherical(20,30,40); // sph = xyz_to_spherical(20,30,40);
// sph = xyz_to_spherical([40,50,70]); // sph = xyz_to_spherical([40,50,70]);
function xyz_to_spherical(x,y=undef,z=undef) = let( // sphs = xyz_to_spherical([[40,50,70], [25,-14,27]]);
p = is_num(x)? [x, default(y,0), default(z,0)] : point3d(x) function xyz_to_spherical(x,y,z) =
) [norm(p), atan2(p.y,p.x), atan2(norm([p.x,p.y]),p.z)]; y != undef
? assert(is_num(x) && is_num(y) && is_num(z), "Bad Arguments.")
[norm([x,y,z]), atan2(y,x), atan2(norm([x,y]),z)]
: assert(is_list(x), "Bad Arguments")
is_num(x.x)
? xyz_to_spherical(x.x, x.y, x.z)
: [for(p = x) xyz_to_spherical(p.x, p.y, p.z)];
// Function: altaz_to_xyz() // Function: altaz_to_xyz()
// Usage: // Usage:
// pt = altaz_to_xyz(alt, az, r); // pt = altaz_to_xyz(alt, az, r);
// pt = altaz_to_xyz([alt, az, r]); // pt = altaz_to_xyz([ALT,AZ,R]);
// pts = altaz_to_xyz([[ALT,AZ,R], [ALT,AZ,R], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), xyz_to_altaz() // See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), xyz_to_altaz()
// Synopsis: Convert altitude/azimuth/range to 3d cartesian coordinates. // Synopsis: Convert altitude/azimuth/range to 3d cartesian coordinates.
// Description: // Description:
// Convert altitude/azimuth/range coordinates to 3D cartesian coordinates. // Convert altitude/azimuth/range coordinates to 3D cartesian coordinates.
// Returns [X,Y,Z] cartesian coordinates. // Called with three arguments, converts the `alt`, `az`, and 'r' 3D altitude-azimuth coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with one `[ALTITUDE,AZIMUTH,RANGE]` vector argument, converts the 3D alt-az coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with a list of `[ALTITUDE,AZIMUTH,RANGE]` vector arguments, converts each 3D alt-az coordinate into `[X,Y,Z]` cartesian coordinates.
// Altitude is the angle above the XY plane, Azimuth is degrees clockwise of Y+ on the XY plane, and Range is the distance from the origin.
// Arguments: // Arguments:
// alt = altitude angle in degrees above the XY plane. // alt = altitude angle in degrees above the XY plane.
// az = azimuth angle in degrees clockwise of Y+ on the XY plane. // az = azimuth angle in degrees clockwise of Y+ on the XY plane.
@ -428,25 +481,31 @@ function xyz_to_spherical(x,y=undef,z=undef) = let(
// Example: // Example:
// xyz = altaz_to_xyz(20,30,40); // xyz = altaz_to_xyz(20,30,40);
// xyz = altaz_to_xyz([40,60,50]); // xyz = altaz_to_xyz([40,60,50]);
function altaz_to_xyz(alt,az=undef,r=undef) = let( function altaz_to_xyz(alt,az,r) =
p = az==undef? alt[0] : alt, az != undef
t = 90 - (az==undef? alt[1] : az), ? assert(is_num(alt) && is_num(az) && is_num(r), "Bad Arguments.")
rad = az==undef? alt[2] : r r*[cos(90-az)*cos(alt), sin(90-az)*cos(alt), sin(alt)]
) rad*[cos(p)*cos(t), cos(p)*sin(t), sin(p)]; : assert(is_list(alt), "Bad Arguments")
is_num(alt.x)
? altaz_to_xyz(alt.x, alt.y, alt.z)
: [for(p = alt) altaz_to_xyz(p.x, p.y, p.z)];
// Function: xyz_to_altaz() // Function: xyz_to_altaz()
// Usage: // Usage:
// alt_az_r = xyz_to_altaz(x,y,z); // alt_az_r = xyz_to_altaz(x,y,z);
// alt_az_r = xyz_to_altaz([X,Y,Z]); // alt_az_r = xyz_to_altaz([X,Y,Z]);
// alt_az_rs = xyz_to_altaz([[X,Y,Z], [X,Y,Z], ...]);
// Topics: Coordinates, Points, Paths // Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz() // See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz()
// Synopsis: Convert 3d cartesian coordinates to [altitude,azimuth,range]. // Synopsis: Convert 3d cartesian coordinates to [altitude,azimuth,range].
// Description: // Description:
// Convert 3D cartesian coordinates to altitude/azimuth/range coordinates. // Converts 3D cartesian coordinates to altitude/azimuth/range coordinates.
// Returns [altitude,azimuth,range], where altitude is angle above the // Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into an `[ALTITUDE,AZIMUTH,RANGE]` coordinate.
// XY plane, azimuth is degrees clockwise of Y+ on the XY plane, and // Called with one `[X,Y,Z]` vector argument, converts the 3D cartesian coordinate into a `[ALTITUDE,AZIMUTH,RANGE]` coordinate.
// range is the distance from the origin. // Called with a list of `[X,Y,Z]` vector arguments, converts each 3D cartesian coordinate into `[ALTITUDE,AZIMUTH,RANGE]` coordinates.
// Altitude is the angle above the XY plane, Azimuth is degrees clockwise of Y+ on the XY plane, and Range is the distance from the origin.
// Arguments: // Arguments:
// x = X coordinate. // x = X coordinate.
// y = Y coordinate. // y = Y coordinate.
@ -454,9 +513,14 @@ function altaz_to_xyz(alt,az=undef,r=undef) = let(
// Example: // Example:
// aa = xyz_to_altaz(20,30,40); // aa = xyz_to_altaz(20,30,40);
// aa = xyz_to_altaz([40,50,70]); // aa = xyz_to_altaz([40,50,70]);
function xyz_to_altaz(x,y=undef,z=undef) = let( function xyz_to_altaz(x,y,z) =
p = is_num(x)? [x, default(y,0), default(z,0)] : point3d(x) y != undef
) [atan2(p.z,norm([p.x,p.y])), atan2(p.x,p.y), norm(p)]; ? assert(is_num(x) && is_num(y) && is_num(z), "Bad Arguments.")
[atan2(z,norm([x,y])), atan2(x,y), norm([x,y,z])]
: assert(is_list(x), "Bad Arguments")
is_num(x.x)
? xyz_to_altaz(x.x, x.y, x.z)
: [for(p = x) xyz_to_altaz(p.x, p.y, p.z)];