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# kumadasu/learningGA_section8-1.md

Created June 17, 2018 03:28
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``````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,
``````
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