Functions List
Coordinate Systems
• xyz
The function xyz defines a position in space specified
by its Cartesian coordinates x, y, and z.
Parameters:
x - Coordinate value for x
y - Coordinate value for y
z - Coordinate value for z
Syntax:
(xyz x y z)
Example:
> (xyz 1 2 3)
#<xyz 1 2 3>
> (xyz (* 2 3) (+ 4 1) (- 6 2))
#<xyz 6 5 4>
• cx
The function cx returns the x coordinate of a given point.
Parameters:
p – Point from which to extract the x coordinate
Syntax:
(cx p)
Example:
> (cx (xyz 1 2 3))
1
> (cx (xyz (* 2 3) (+ 4 1) (- 6 2)))
6
• cy
The function cy returns the y coordinate of a given point.
Parameters:
p – Point from which to extract the y coordinate
Syntax:
(cy p)
Example:
> (cy (xyz 1 2 3))
2
> (cy (xyz (* 2 3) (+ 4 1) (- 6 2)))
5
• cz
The function cz returns the z coordinate of a given point.
Parameters:
p – Point from which to extract the z coordinate
Syntax:
(cz p)
Example:
> (cz (xyz 1 2 3))
3
> (cz (xyz (* 2 3) (+ 4 1) (- 6 2)))
4
• x
The function x defines a position in space specified only
by its x coordinate, meaning the position will be located along the X axis. The remaining
coordinates are null.
Parameters:
n – Coordinate value for x
Syntax:
(x n)
Example:
> (x 5)
#<xyz:5 0 0>
• y
The function y defines a position in space specified only
by its y coordinate, meaning the position will be located along the Y axis. The remaining
coordinates are null.
Parameters:
n – Coordinate value for y
Syntax:
(y n)
Example:
> (y 3)
#<xyz:0 3 0>
• z
The function z defines a position in space specified only
by its z coordinate, meaning the position will be located along the Z axis. The remaining
coordinates are null.
Parameters:
n – Coordinate value for z
Syntax:
(z n)
Example:
> (z 10)
#<xyz:0 0 10>
• xy
The function xy defines a position in space specified by
its x and y coordinates, meaning the position will be located on the XY plane. The z
coordinate is null.
Parameters:
x – Coordinate value for x
y - Coordinate value for y
Syntax:
(xy x y)
Example:
> (xy 2 5)
#<xyz:2 5 0>
> (xy 0 0)
#<xyz:0 0 0>
• xz
The function xz defines a position in space specified
by its x and z coordinates, meaning the position will be located on the XZ plane. The y
coordinate is null.
Parameters:
x – Coordinate value for x
z - Coordinate value for z
Syntax:
(xz x z)
Example:
> (xz 1 8)
#<xyz:1 0 8>
• yz
The function yz defines a position in space specified by
its y and z coordinates, meaning the position will be located on the YZ plane. The x coordinate
is null.
Parameters:
y – Coordinate value for y
z - Coordinate value for z
Syntax:
(yz y z)
Example:
> (yz 3 7)
#<xyz:0 3 7>
• +xyz
Given a position in space, the function +xyz will define a
new position by applying a translation vector to all its coordinates.
Parameters:
p – Original point in space
dx – Translation value for the x coordinate
dy – Translation value for the y coordinate
dz – Translation value for the z coordinate
Syntax:
(+xyz p dx dy dz)
Example:
> (+xyz (xyz 0 0 0) 1 2 3)
#<xyz:1 2 3>
> (+xyz (xyz 1 2 3) 4 5 6)
#<xyz:5 7 9>
• +x
Given a position in space, the function +x will define a
new position by applying a translation vector to the x coordinate only. The y and z coordinates
of the original position remain unaltered.
Parameters:
p – Original point in space
dx – Translation value for the x coordinate
Syntax:
(+x p dx)
Example:
> (+x (xyz 0 0 0) 5))
#<xyz:5 0 0>
• +y
Given a position in space, the function +y will define a
new position by applying a translation vector to the y coordinate only. The x and z coordinates
of the original position remain unaltered.
Parameters:
p – Original point in space
dy – Translation value for the y coordinate
Syntax:
(+y p dy)
Example:
> (+y (xyz 1 2 3) 5))
#<xyz:1 7 3>
• +z
Given a position in space, the function +z will define a new
position by applying a translation vector to the z coordinate only. The x and y coordinates
of the original position remain unaltered.
Parameters:
p – Original point in space
dz – Translation value for the z coordinate
Syntax:
(+z p dz)
Example:
> (+z (xyz 1 2 3) 3))
#<xyz:1 2 6>
• +xy
Given a position in space, the function +xy will define a new
position by applying a translation vector to its x and y coordinates. The z coordinate of the
original position remains unaltered.
Parameters:
p – Original point in space
dx – Translation value for the x coordinate
dy – Translation value for the y coordinate
Syntax:
(+xy p dx dy)
Example:
> (+xy (xyz 1 2 3) 1 3))
#<xyz:2 5 3>
• +xz
Given a position in space, the function +xz will define a new
position by applying a translation vector to its x and z coordinates. The y coordinate of the
original position remains unaltered.
Parameters:
p – Original point in space
dx – Translation value for the x coordinate
dz – Translation value for the z coordinate
Syntax:
(+xz p dx dz)
Example:
> (+xz (xyz 1 2 3) 1 5))
#<xyz:2 2 8>
• +yz
Given a position in space, the function +yz will define a new
position by applying a translation vector to its y and z coordinates. The x coordinate of the
original position remains unaltered.
Parameters:
p – Original point in space
dy – Translation value for the y coordinate
dz – Translation value for the z coordinate
Syntax:
(+yz p dy dz)
Example:
> (+yz (xyz 2 1 5) 1 2))
#<xyz:2 2 7>
• pol
The function pol defines a position in space specified by its
polar coordinates, i.e., specified by a radius and an angle with the X axis. The height of the
position will be null.
Parameters:
rho – Polar radius
phi – Polar angle with the X axis
Syntax:
(pol rho phi)
Example:
> (pol 1 0)
#<xyz 1 0 0>
> (pol (sqrt 2) (/ pi 4))
#<xyz 1.0000000000000002 1.0 0>
> (pol 1 (/ pi 2))
#<xyz 6.123233995736766e-017 1.0 0>
> (pol 1 pi)
#<xyz -1.0 1.2246467991473532e-016 0>
• pol-rho
Given a position in space, the function pol-rho returns the
distance of that position to the UCS origin.
Parameters:
p – Position in space
Syntax:
(pol-rho p)
Example:
> (pol-rho (pol 10 (/ pi 3)))
10.0
> (pol-rho (xyz 1 2 3))
2.23606797749979
• pol-phi
Given a position in space, the function pol-phi
returns the angle value of that position with the X axis.
Parameters:
p – Position in space
Syntax:
(pol-phi p)
Example:
> (pol-phi (pol 10 (/ pi 3)))
1.0471975511965976
> (pol-phi (xyz 1 2 3))
1.1071487177940904
• +pol
Given a position in space, the function +pol will define a new
position by applying a translation vector specified by its intensity and direction. The z
coordinate remains unaltered.
Parameters:
p – Position in space
drho – Vector intensity
dphi – Vector direction
Syntax:
(+pol p drho dphi)
Example:
> (+pol (xy 1 2) (sqrt 2) (/ pi 4))
#<xyz 2.0 3.0 0>
> (+pol (xy 1 2) 1 0)
#<xyz 2 2 0>
> (+pol (xy 1 2) 1 (/ pi 2))
#<xyz 1.0 3.0 0>
• cyl
The function cyl defines a position in space specified
by its cylindrical coordinates, i.e., a radius, an angle with the X axis and a height value.
Parameters:
rho – Polar radius
phi – Polar angle with the X axis
z – Height value
Syntax:
(cyl rho phi z)
Example:
> (cyl 5 0 10)
#<xyz:5 0 10>
• cyl-rho
Given a position in space, the function cyl-rho
returns the distance of that position to the UCS origin. If the position is
specified in cylindrical coordinates it returns the rho component.
Parameters:
p – Position in space
Syntax:
(cyl-rho p)
Example:
> (cyl-rho (xyz 1 5 8))
5.0990195135927845
> (cyl-rho (cyl 5 pi/2 8))
5.0
> (cyl-rho (pol 2 pi/3))
2.0
• cyl-phi
Given a position in space, the function cyl-phi
returns the angle value of that position with the X axis. If the position is
specified in cylindrical coordinates it returns the phi component.
Parameters:
p – Position in space
Syntax:
(cyl-phi p)
Example:
> (cyl-phi (xyz 1 5 8))
1.373400766945016
> (cyl-phi (cyl 5 pi/2 8))
1.5707963267948966
> (cyl-phi (cyl 5 1.7 8))
1.7
• cyl-z
Given a position in space, the function cyl-z
returns the height value of that position. If the position is
specified in cylindrical coordinates it returns the z component.
Parameters:
p – Position in space
Syntax:
(cyl-z p)
Example:
> (cyl-z (xyz 0 5 3))
3
> (cyl-z (cyl 4 pi/6 -5))
-5
> (cyl-z (pol 10 pi/4))
0
• +cyl
Given a position in space, the function +cyl) will define
a new position by applying a translation vector specified by its intensity, direction and
height.
Parameters:
p – Original position in space
drho – Vector intensity
dphi – Vector direction
dz – Height change
Syntax:
(+cyl p drho dphi dz)
Example:
> (+cyl (xyz 1 2 3) 3 pi/6 5)
#<xyz:3.598076211353316 3.5 8>
• sph
The function sph defines a position in space specified
in spherical coordinates, i.e., a radius, the longitude (azimuth) and polar angle (zenith).
Parameters:
rho – Radius
phi – Longitude
psi – Polar angle
Syntax:
(sph rho phi psi)
Example:
> (sph (sqrt 3) pi/4 (atan (sqrt 2)))
#<xyz:1.0 0.9... 0.9...>
• sph-rho
Given a position in space, the function sph-rho
returns the distance of that position to the UCS origin. If the position is specified
in spherical coordinates it returns the rho component.
Parameters:
p - Position in space
Syntax:
(sph-rho p)
Example:
> (sph-rho (sph 2 pi/3 pi/4))
2.0
> (sph-rho (cyl 10 pi 5))
11.180339887498949
• sph-phi
Given a position in space, the function sph-phi
returns the angle value of that position with the X axis. If the position is
specified in spherical coordinates it returns the phi component.
Parameters:
p - Position in space
Syntax:
(sph-phi p)
Example:
> (sph-phi (xyz 2 2 10))
0.7853981633974483
> (sph-phi (sph 2 pi pi/6))
3.141592653589793
> (sph-phi (cyl 5 1.2 -5))
1.2
• sph-spi
Given a position in space, the function sph-psi
returns the polar angle of that position, i.e., the angle measured from the azimuth
reference direction to the orthogonal projection of the line segment origin-position
on the reference plane. If the position is specified in spherical coordinates it returns
the psi component.
Parameters:
p - Position in space
Syntax:
(sph-psi p)
Example:
> (sph-psi (sph 5 pi/2 pi/4))
0.7853981633974483
> (sph-psi (sph 10 0 5.2))
1.0831853071795863
> (sph-psi (cyl 4.2 -pi/3 3.1))
0.9349579032711515
• +sph
Given a position in space, the function +sph will define
a new position by applying a translation vector specified by its intensity, longitudinal
direction and polar direction.
Parameters:
p – Original position in space
drho – Vector intensity
dphi – Longitudinal direction
dpsi – Polar direction
Syntax:
(+sph p drho dphi dpsi)
Example:
> (+sph (xyz 1 2 3) 4 pi/4 pi/3)
#<xyz:3.4494897427831783 4.449489742783178 5.0>
• +rho
Given a position in space, the function +rho will add a
radial distance to that specified position.
Parameters:
p - Original position
rho - Radial distance
Syntax:
(+rho p rho)
Example:
> (+rho (xyz 1 2 0) 5)
#<xyz:3.2360679774997902 6.47213595499958 0>
> (+rho (cyl 5 pi/4 10) 5)
#<xyz:7.0710678118654755 7.071067811865475 10>
> (+rho (cyl 5 0 10) 2)
#<xyz:7 0 10>
• +phi
Given a position in space, the function +phi will add a polar
angle to that specified position.
Parameters:
p - Original position
phi - Polar angle
Syntax:
(+phi p phi)
Example:
> (+psi (sph 5 0 pi/4) pi/3)
#<xyz:4.8296291314453415 0.0 -1.2940952255126033>
> (+psi (cyl 5 0 2) pi/2)
#<xyz:2.0000000000000004 0 -5.0>
• +psi
Given a position in space, the function +psi will add
an azimuth angle to that specified position.
Parameters:
p - Original position
psi - Azimuth angle
Syntax:
(+psi p psi)
Example:
> (+psi (cyl 5 0 2) pi/2)
#<xyz:2.0000000000000004 0 -5.0>
> (+psi (sph 10 0 pi) pi)
#<xyz:-2.4492935982947065e-015 -0.0 10.0>
> (+psi (xyz 0 0 0) pi/2)
#<xyz:0 0 0>
> (+psi (xyz 1 1 0) pi/4)
#<xyz:0.7071067811865477 0.7071067811865476 -1.0>
• roundc
The function roundc rounds the coordinates of a specified
position up or down depending on the decimal value.
Parameters:
p - Position
Syntax:
(roundc p)
Example:
> (roundc (xyz 1.5 2.2 0.1))
#<xyz:2.0 2.0 0.0>
> (roundc (xyz 1.00000002 2.00521 0.0000015))
#<xyz:1.0 2.0 0.0>
• =c?
The function =c? tests is two given coordinates are coincidental,
returning #t if they are and #f if they are not. Be aware that due to round off errors two positions
might not be tested for #t even when they appear to be coincidental (see last example). For that make
sure to use the function roundc first.
Parameters:
p1 - First position
p2 - Second position
Syntax:
(=c? p1 p2)
(=c? (roundc p1) (roundcp2))
Example:
> (=c? (xyz 5 6 0) (xy 5 6))
#t
> (=c? (xyz 3 0 5) (xyz 0 -8 7))
#f
> (=c? (cyl 5.0 pi/2 0.0) (pol 5.0 pi/2))
#t
> (=c? (xy 0 5) (pol 5 pi/2))
#f
> (=c? (roundc (xy 0 5)) (roundc (pol 5 pi/2)))
#t
• xyz-on
The function xyz-on sets a new UCS by specifying the
origin position and both the X and Y axes. The Y axis doesn't have to be perpendicular to
the X axis.
Parameters:
o - Origin point
x - X axis
y - Y axis
Syntax:
(xyz-on o x y)
Example:
> (rectangle (xyz-on (xyz 0 0 0) (uxy) (uy)) 10 5)
#<rectangle 0>
• xyz-on-z-rot
The function xyz-on-z-rot rotates the UCS by a specified angle along the the Z axis.
The X and Y axes remain perpendicular to each other.
Parameters:
p - Origin point
a - Rotation angle
Syntax:
(xyz-on-z-rot p a)
Example:
>(rectangle (xyz-on-z-rot (xyz 0 0 0) pi/4) 10 5)
#<rectangle 0>