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peko/R201.nim

Created September 14, 2024 21:35
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R201.nim
# #define PI 3.14159265358979323846
# static const char* basis[] = { "1","e0","e1","e2","e01","e20","e12","e012" };
from std/math import sqrt
type
PGA2D* = array[8, float64]
proc `~`* (a:PGA2D):PGA2D =
result[0] = a[0]
result[1] = a[1]
result[2] = a[2]
result[3] = a[3]
result[4] = -a[4]
result[5] = -a[5]
result[6] = -a[6]
result[7] = -a[7]
proc `!`* (a:PGA2D):PGA2D =
result[0] = a[7]
result[1] = a[6]
result[2] = a[5]
result[3] = a[4]
result[4] = a[3]
result[5] = a[2]
result[6] = a[1]
result[7] = a[0]
proc conjugate* (a:PGA2D):PGA2D =
result[0] = a[0]
result[1] = -a[1]
result[2] = -a[2]
result[3] = -a[3]
result[4] = -a[4]
result[5] = -a[5]
result[6] = -a[6]
result[7] = a[7]
proc involute* (a:PGA2D):PGA2D =
result[0] = a[0]
result[1] = -a[1]
result[2] = -a[2]
result[3] = -a[3]
result[4] = a[4]
result[5] = a[5]
result[6] = a[6]
result[7] = -a[7]
proc `*`* (a:PGA2D, b:PGA2D):PGA2D =
result[0] = b[0]*a[0]+b[2]*a[2]+b[3]*a[3]-b[6]*a[6];
result[1] = b[1]*a[0]+b[0]*a[1]-b[4]*a[2]+b[5]*a[3]+b[2]*a[4]-b[3]*a[5]-b[7]*a[6]-b[6]*a[7];
result[2] = b[2]*a[0]+b[0]*a[2]-b[6]*a[3]+b[3]*a[6];
result[3] = b[3]*a[0]+b[6]*a[2]+b[0]*a[3]-b[2]*a[6];
result[4] = b[4]*a[0]+b[2]*a[1]-b[1]*a[2]+b[7]*a[3]+b[0]*a[4]+b[6]*a[5]-b[5]*a[6]+b[3]*a[7];
result[5] = b[5]*a[0]-b[3]*a[1]+b[7]*a[2]+b[1]*a[3]-b[6]*a[4]+b[0]*a[5]+b[4]*a[6]+b[2]*a[7];
result[6] = b[6]*a[0]+b[3]*a[2]-b[2]*a[3]+b[0]*a[6];
result[7] = b[7]*a[0]+b[6]*a[1]+b[5]*a[2]+b[4]*a[3]+b[3]*a[4]+b[2]*a[5]+b[1]*a[6]+b[0]*a[7];
proc `^`* (a:PGA2D, b:PGA2D):PGA2D =
result[0] = b[0]*a[0];
result[1] = b[1]*a[0]+b[0]*a[1];
result[2] = b[2]*a[0]+b[0]*a[2];
result[3] = b[3]*a[0]+b[0]*a[3];
result[4] = b[4]*a[0]+b[2]*a[1]-b[1]*a[2]+b[0]*a[4];
result[5] = b[5]*a[0]-b[3]*a[1]+b[1]*a[3]+b[0]*a[5];
result[6] = b[6]*a[0]+b[3]*a[2]-b[2]*a[3]+b[0]*a[6];
result[7] = b[7]*a[0]+b[6]*a[1]+b[5]*a[2]+b[4]*a[3]+b[3]*a[4]+b[2]*a[5]+b[1]*a[6]+b[0]*a[7];
proc `&`* (a:PGA2D, b:PGA2D):PGA2D =
result[7] = 1*(a[7]*b[7]);
result[6] = 1*(a[6]*b[7]+a[7]*b[6]);
result[5] = 1*(a[5]*b[7]+a[7]*b[5]);
result[4] = 1*(a[4]*b[7]+a[7]*b[4]);
result[3] = 1*(a[3]*b[7]+a[5]*b[6]-a[6]*b[5]+a[7]*b[3]);
result[2] = 1*(a[2]*b[7]-a[4]*b[6]+a[6]*b[4]+a[7]*b[2]);
result[1] = 1*(a[1]*b[7]+a[4]*b[5]-a[5]*b[4]+a[7]*b[1]);
result[0] = 1*(a[0]*b[7]+a[1]*b[6]+a[2]*b[5]+a[3]*b[4]+a[4]*b[3]+a[5]*b[2]+a[6]*b[1]+a[7]*b[0]);
proc `|`* (a:PGA2D, b:PGA2D):PGA2D =
result[0] = b[0]*a[0]+b[2]*a[2]+b[3]*a[3]-b[6]*a[6];
result[1] = b[1]*a[0]+b[0]*a[1]-b[4]*a[2]+b[5]*a[3]+b[2]*a[4]-b[3]*a[5]-b[7]*a[6]-b[6]*a[7];
result[2] = b[2]*a[0]+b[0]*a[2]-b[6]*a[3]+b[3]*a[6];
result[3] = b[3]*a[0]+b[6]*a[2]+b[0]*a[3]-b[2]*a[6];
result[4] = b[4]*a[0]+b[7]*a[3]+b[0]*a[4]+b[3]*a[7];
result[5] = b[5]*a[0]+b[7]*a[2]+b[0]*a[5]+b[2]*a[7];
result[6] = b[6]*a[0]+b[0]*a[6];
result[7] = b[7]*a[0]+b[0]*a[7];
proc `+`* (a:PGA2D, b:PGA2D):PGA2D =
result[0] = a[0]+b[0]
result[1] = a[1]+b[1]
result[2] = a[2]+b[2]
result[3] = a[3]+b[3]
result[4] = a[4]+b[4]
result[5] = a[5]+b[5]
result[6] = a[6]+b[6]
result[7] = a[7]+b[7]
proc `-`* (a:PGA2D, b:PGA2D):PGA2D =
result[0] = a[0]-b[0]
result[1] = a[1]-b[1]
result[2] = a[2]-b[2]
result[3] = a[3]-b[3]
result[4] = a[4]-b[4]
result[5] = a[5]-b[5]
result[6] = a[6]-b[6]
result[7] = a[7]-b[7]
proc `*`* (a:PGA2D, s:float64):PGA2D =
result[0] = a[0]*s
result[1] = a[1]*s
result[2] = a[2]*s
result[3] = a[3]*s
result[4] = a[4]*s
result[5] = a[5]*s
result[6] = a[6]*s
result[7] = a[7]*s
proc `*`* (s:float64,a:PGA2D):PGA2D = a*s
proc `+`* (a:PGA2D, s:float64):PGA2D =
result[0] = a[0]+s
result[1] = a[1]
result[2] = a[2]
result[3] = a[3]
result[4] = a[4]
result[5] = a[5]
result[6] = a[6]
result[7] = a[7]
proc `+`* (s:float64, a:PGA2D):PGA2D = a+s
proc `-`* (a:PGA2D, s:float64):PGA2D =
result[0] = a[0]-s
result[1] = a[1]
result[2] = a[2]
result[3] = a[3]
result[4] = a[4]
result[5] = a[5]
result[6] = a[6]
result[7] = a[7]
proc `-`* (s:float64, a:PGA2D):PGA2D =
result[0] = s-a[0]
result[1] = -a[1]
result[2] = -a[2]
result[3] = -a[3]
result[4] = -a[4]
result[5] = -a[5]
result[6] = -a[6]
result[7] = -a[7]
proc norm(a:PGA2D):float64 = sqrt(abs(conjugate(a)[0]))
proc inorm(a:PGA2D):float64 = norm(!a)
proc normalized(a:PGA2D):PGA2D = a*(1.0/norm(a))
proc point*(x,y:float64):PGA2D = [ 0.0, 0.0, 0.0, 0.0, y, x, 1.0, 0.0]
proc line* (a,b,c:float64):PGA2D = [ 0.0, c, a, b, 0.0, 0.0, 0.0, 0.0]
let
e0* :PGA2D = [0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0]
e1* :PGA2D = [0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0]
e2* :PGA2D = [0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0]
e01* :PGA2D = [0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0]
e20* :PGA2D = [0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0]
e12* :PGA2D = [0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0]
e012*:PGA2D = [0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0]
var
a:PGA2D = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]
b:PGA2D = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]
s:float64 = 0.5
echo "(a):" & $(a)
echo "(~a):" & $(~a)
echo "(!a):" & $(!a)
echo "(conjugate a):" & $(conjugate a)
echo "(involute a):" & $(involute a)
echo "(a*b):" & $(a*b)
echo "(a^b):" & $(a^b)
echo "(a&b):" & $(a&b)
echo "(a|b):" & $(a|b)
echo "(a+b):" & $(a+b)
echo "(a-b):" & $(a-b)
echo "(a+b):" & $(a+b)
echo "(a*s):" & $(a*s)
echo "(s*a):" & $(s*a)
echo "(a+s):" & $(a+s)
echo "(s+a):" & $(s+a)
echo "(a-s):" & $(a-s)
echo "(s-a):" & $(s-a)
echo "(norm(a)):" & $(norm(a))
echo "(inorm(a)):" & $(inorm(a))
echo "(normalized(a)):" & $(normalized(a))
var
l = line(1.0, 1.0, 1.0)
p = point(1.0, 1.0)
pr = normalized((p|l)*(~l))
echo "line:" & $(l)
echo "point:" & $(p)
echo "projection :" & $(pr)
# // 3D Projective Geometric Algebra
# // Written by a generator written by enki.
# #include <stdio.h>
# #include <cmath>
# #include <array>
# int main (int argc, char **argv) {
# printf("e0*e0 : "); (e0*e0).log();
# printf("pss : "); e012.log();
# printf("pss*pss : "); (e012*e012).log();
# return 0;
# }
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