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Geometry 179
inversion
Draws the inversion of a point, with respect to another point,
by a scale factor.
inversion(point1, realk, point2)
Example:
inversion(GA, 3, GB) draws point C on line AB such
that AB*AC=3. In this case, point A is the center of the
inversion and the scale factor is 3. Point B is the point whose
inversion is created.
In general, the inversion of point A through center C, with
scale factor k, maps A onto A’, such that A’ is on line CA and
CA*CA’=k, where CA and CA’ denote the lengths of the
corresponding segments. If k=1, then the lengths CA and CA’
are reciprocals.
projection
Draws the orthogonal projection of a point onto a curve.
projection(curve, point)
reflection
Reflects a geometric object over a line or through a point. The
latter is sometimes referred to as a half-turn.
reflection(line, object) or reflection(point,
object)
Examples:
reflection(line(x=3),point(1,1)) reflects the
point at (1, 1) over the vertical line x=3 to create a point at
(5,1).
reflection(1+i, 3-2i) reflects the point at (3,–2)
through the point at (1, 1) to create a point at (–1, 4).