幾何学と代数系8章〜8.6.2節までをGAViewerで触った際のメモ

learningGA_section8-1.md

batch initialize() {
	clf(),
	default_model(c3ga),

	p0 = black(c3ga_point(0,0,0)),
	p1 = red(c3ga_point(-1,-1,-1)),
	p2 = green(c3ga_point(-1,-1, 1)),
	p3 = blue(c3ga_point( 1,-1, 1)),
	p4 = yellow(c3ga_point( 1, 1, 1)),
}

8.3 Grassmann algebra in conformal space

initialize(),

# line
p1^p2^ni,

# plane
p1^p2^p3^ni,

#　circle
p1^p2^p3,

# sphere
p1^p2^p3^p4,

8.5 Cliford algebra in conformal space

8.5.2 Translator

initialize(),
t = 0.5 e1 + 0.5 e2 + 0.5 e3,
Tt = 1 - 1/2 t ni,

Tt p1 / Tt,

Tt = exp (- 1/2 t ni),

8.5.3 Rotor

initialize(),

x = e1; y = e2;
R = y x,
R p1 / R,

8.6 Conformal geometry

8.6.2 Reflector

initialize(),
n = e1;
h = 0.5;
mypi = n + h ni,
- mypi p1 / mypi,
- mypi p4 / mypi,


# rotator
n2 = e2;
mypi2 = n2 + h ni,

mypi3 = mypi mypi2,
mypi3 p1 mypi3,
mypi3 p4 mypi3,