2DPGA: Project and reject

This example shows how to perform projection and rejection, using 2DPGA.

Based on https://enkimute.github.io/ganja.js/examples/coffeeshop.html#pga2d_project_and_reject.

First we create 2DPGA, and add its basis blades to the local namespace.

from kingdon import Algebra

alg = Algebra(2, 0, 1)
locals().update(alg.blades)

Next, make formulas to construct points and lines from coefficients, and to project and reject any elements of geometry.

# Construct points and lines from coefficients
point = lambda x, y: (e0 + x*e1 + y*e2).dual()
line = lambda a, b, c: a*e1 + b*e2 + c*e0

# The formulas for projection and rejection are the same for all elements of geometry in PGA
project = lambda a, b: (a | b) / b
reject = lambda a, b: (a | b)

Construct the points \(A\), \(B\), and \(C\), and make the line \(AC\) by joining \(A\) and \(C\).

A = point(1, 1)
B = point(-1, 1)
C = point(-1, -1)
AC = A & C

alg.graph(
    0xD0FFE1, [A,B,C],
    0x882288, project(B, AC), "project B onto AC",
    0x882288, project(AC, B), "project AC onto B",
    0x008844, reject(AC, B),  "reject AC from B",
    0x00AA88, AC, "AC",
    0x224488, A, "A", B, "B", C, "C",
    lineWidth=3, grid=1, labels=1
)