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Function Reference: geom.transform

drafting: Q = geom.transform (P, T)
drafting: Q = geom.transform (P, OP, VAL)
drafting: Q = geom.transform (P, OP, VAL, CENTRE)

Apply a planar transformation to a set of points.

Q = geom.transform (P, T) applies the 3-by-3 homogeneous matrix T to every row of the N-by-2 matrix P and returns the result in the same shape. T acts on column vectors [x; y; 1], which is the usual convention, so transformations compose by ordinary matrix multiplication with the last-applied factor on the left.

Q = geom.transform (P, OP, VAL) builds the matrix from a named operation instead. OP is one of:

  • 'translate' — VAL is a 1-by-2 offset [dx, dy].
  • 'rotate' — VAL is an angle in degrees, counter-clockwise positive. Degrees rather than radians because this is a drafting package and drawings are dimensioned in degrees.
  • 'scale' — VAL is a scalar factor, or a 1-by-2 pair [sx, sy] for an anisotropic scaling.
  • 'mirror' — VAL is 'x' or 'y', naming the axis to reflect about. Mirroring about 'x' negates the y coordinate, so the point [1, 2] becomes [1, -2].

Q = geom.transform (P, OP, VAL, CENTRE) performs the operation about the point CENTRE rather than the origin. It applies to 'rotate', 'scale' and 'mirror'; a translation is unaffected by any centre, so supplying one is an error rather than a silently ignored argument.

Unlike most of this namespace, geom.transform accepts any point set, not only a polygon: two points making up a single edge are valid input.

See also: geom.bbox, geom.offset

Source Code: geom.transform

The four named operations, each shown against the original. A centre may be given so the operation happens about a point rather than the origin.

 P = [0, 0; 30, 0; 30, 10; 10, 10; 10, 20; 0, 20];
 D = draw.Drawing ().polyline (P, true);
 D.Colour = 'red';
 D = D.polyline (geom.transform (P, 'translate', [45, 0]), true);
 D.Colour = 'blue';
 D = D.polyline (geom.transform (P, 'rotate', 90, [15, 10]), true);
 D.Colour = 'green';
 D = D.polyline (geom.transform (P, 'scale', 0.5, [15, 10]), true);
 D.Colour = 'magenta';
 D = D.polyline (geom.transform (P, 'mirror', 'y'), true);
 plot (D);
 title ('translate, rotate about a point, scale, mirror');
plotted figure

A 3-by-3 homogeneous matrix does anything the named operations do and composes by ordinary multiplication, last-applied on the left.

 P = [0, 0; 20, 0; 20, 10];
 T = [1, 0, 50; 0, 1, 0; 0, 0, 1] * [0, -1, 0; 1, 0, 0; 0, 0, 1];
 geom.transform (P, T)
ans =

   50    0
   50   20
   40   20