COORDINATE TRANSFORMATIONS
This chapter tells you about the types of transformations available in GDL (moving, scaling, rotating the coordinate system) and the way they are interpreted and managed.
About Transformations
In GDL, all the geometric elements are linked strictly to the local coordinate system. GDL uses a right-handed coordinate system. For example, one corner of a block is in the origin and its sides are in the x-y, x-z and y-z planes.
Placing a geometric element in the desired position requires two steps. First, move the coordinate system to the desired position. Second, generate the element. Every movement, rotation or stretching of the coordinate system along or around an axis is called a transformation.
Transformations are stored in a stack; interpretation starts from the last one backwards. Scripts inherit this stack; they can insert new elements onto it but can only delete the locally defined ones. It is possible to delete one, more or all of the transformations defined in the current script. After returning from a script, the locally defined transformations are removed from the stack.
2D TRANSFORMATIONS
These are the equivalents in the 2D space of the ADD, MUL and ROTZ 3D transformations.
ADD2
ADD2 x, y
Example:
ADD2 a, b
Y
Y
X
b
X
a
MUL2
MUL2 x, y
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Coordinate Transformations
ROT2
ROT2 alpha
Example:
ROT2 beta
Y
Y
X
beta
X
3D TRANSFORMATIONS
ADDX
ADDX dx
ADDY
ADDY dy
ADDZ
ADDZ dz
Moves the local coordinate system along the given axis by dx, dy or dz respectively.
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Coordinate Transformations
ADD
ADD dx, dy, dz
Replaces the sequence ADDX dx: ADDY dy: ADDZ dz.
It has only one entry in the stack, thus it can be deleted with DEL 1.
Example:
ADD a,b,c
Z
Y
Z
Y |
c |
|
X
b
a
X
MULX
MULX mx
MULY
MULY my
MULZ
MULZ mz
Scales the local coordinate system along the given axis. Negative mx, my, mz means simultaneous mirroring.
MUL
MUL mx, my, mz
Replaces the sequence MULX mx: MULY my: MULZ mz. It has only one entry in the stack, thus it can be deleted with DEL 1.
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Coordinate Transformations
ROTX
ROTX alphax
ROTY
ROTY alphay
ROTZ
ROTZ alphaz
Rotates the local coordinate system around the given axis by alphax, alphay, alphaz degrees respectively, counterclockwise.
Example:
Z
Y
Y
X
beta
X
ROTZ beta
ROT
ROT x, y, z, alpha
Rotates the local coordinate system around the axis defined by the vector (x, y, z) by alpha degrees, counterclockwise. It has only one entry in the stack, thus it can be deleted with DEL 1.
XFORM
XFORM a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34
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