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inner and outer products

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This commit is contained in:
David Allemang
2018-04-03 23:40:06 -04:00
parent 3611b34a4c
commit 8bec0d6b80
3 changed files with 166 additions and 27 deletions
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12
Tetrahedrons/MVec3d.cs
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@@ -68,17 +68,7 @@ namespace Tetrahedrons
return new MVec3D(0, 0, 0, 0, 0, 0, 0, e123);
}
public static MVec3D Complex(double real, double imag)
{
return new MVec3D(real, 0, 0, 0, 0, 0, 0, imag);
}
public static MVec3D Complex(double w, double i, double j, double k)
{
return new MVec3D(w, 0, 0, 0, i, j, k, 0);
}
public static MVec3D Complex(double angle, MVec3D plane)
public static MVec3D Rotor(double angle, MVec3D plane)
{
return Math.Cos(angle) + Math.Sin(angle) * plane;
}

177
Tetrahedrons/MVec4D.cs
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@@ -1,8 +1,11 @@
using System;
using System.Collections.Generic;
using System.Data.SqlClient;
using System.Dynamic;
using System.Runtime.Remoting.Messaging;
using System.Text;
using OpenTK;
using OpenTK.Graphics.ES30;
namespace Tetrahedrons
{
@@ -38,7 +41,26 @@ namespace Tetrahedrons
Xyw * Xyw + Xzw * Xzw + Yzw * Yzw + Xyzw * Xyzw;
public double Norm => Math.Sqrt(Norm2);
public MVec4D Grade(int k)
{
switch (k)
{
case 0:
return Vec0(S);
case 1:
return Vec1(X, Y, Z, W);
case 2:
return Vec2(Xy, Xz, Xw, Yz, Yw, Zw);
case 3:
return Vec3(Xyz, Xyw, Xzw, Yzw);
case 4:
return Vec4(Xyzw);
default:
return Zero;
}
}
#region Swizzle
public double Yx
@@ -904,25 +926,152 @@ namespace Tetrahedrons
);
}
public static MVec4D? Div(MVec4D m, MVec4D n)
{
var inv = n.Inv;
if (!inv.HasValue)
return null;
return Mul(m, inv.Value);
}
public static MVec4D? Div(MVec4D m, MVec4D n) => Mul(m, n.Inv);
public static MVec4D Div(MVec4D m, double c) => Mul(m, 1 / c);
public static MVec4D? Div(double c, MVec4D m)
public static MVec4D? Div(double c, MVec4D n) => Mul(c, n.Inv);
public static MVec4D Inner(MVec4D m, MVec4D n)
{
var inv = m.Inv;
if (!inv.HasValue)
return null;
return Mul(c, inv.Value);
var m0 = m.Grade(0);
var m1 = m.Grade(1);
var m2 = m.Grade(2);
var m3 = m.Grade(3);
var m4 = m.Grade(4);
var n0 = n.Grade(0);
var n1 = n.Grade(1);
var n2 = n.Grade(2);
var n3 = n.Grade(3);
var n4 = n.Grade(4);
return new MVec4D(
m0 * n0 + m1 * n1 + m2 * n2 + m3 * n3 + n4 * n4,
m0 * n1 + m1 * n2 + m2 * n3 + m3 * n4,
m0 * n2 + m1 * n3 + m2 * n4,
m0 * n3 + m1 * n4,
m0 * n4
);
}
public static MVec4D Inner(MVec4D m, double c) => Mul(m, c);
public static MVec4D Inner(double c, MVec4D n) => Mul(c, n);
public static MVec4D Outer(MVec4D m, MVec4D n)
{
var m0 = m.Grade(0);
var m1 = m.Grade(1);
var m2 = m.Grade(2);
var m3 = m.Grade(3);
var m4 = m.Grade(4);
var n0 = n.Grade(0);
var n1 = n.Grade(1);
var n2 = n.Grade(2);
var n3 = n.Grade(3);
var n4 = n.Grade(4);
return new MVec4D(
m0 * n0,
m1 * n0 + m0 * n1,
m2 * n0 + m1 * n1 + m0 * n2,
m3 * n0 + m2 * n1 + m1 * n2 + m0 * n3,
m4 * n0 + m3 * n1 + m2 * n2 + m1 * n3 + m0 * n4
);
}
public static MVec4D Outer(MVec4D m, double c) => Mul(m, c);
public static MVec4D Outer(double c, MVec4D n) => Mul(c, n);
public static MVec4D? Add(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Add(m.Value, n.Value) : null;
public static MVec4D? Add(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Add(m.Value, n.Value) : null;
public static MVec4D? Add(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Add(m.Value, n.Value) : null;
public static MVec4D? Sub(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Sub(m.Value, n.Value) : null;
public static MVec4D? Sub(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Sub(m.Value, n.Value) : null;
public static MVec4D? Sub(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Sub(m.Value, n.Value) : null;
public static MVec4D? Mul(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Mul(m.Value, n.Value) : null;
public static MVec4D? Mul(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Mul(m.Value, n.Value) : null;
public static MVec4D? Mul(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Mul(m.Value, n.Value) : null;
public static MVec4D? Div(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Div(m.Value, n.Value) : null;
public static MVec4D? Div(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Div(m.Value, n.Value) : null;
public static MVec4D? Div(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Div(m.Value, n.Value) : null;
public static MVec4D? Inner(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Inner(m.Value, n.Value) : null;
public static MVec4D? Inner(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Inner(m.Value, n.Value) : null;
public static MVec4D? Inner(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Inner(m.Value, n.Value) : null;
public static MVec4D? Outer(MVec4D? m, MVec4D? n) => m.HasValue && n.HasValue ? (MVec4D?) Outer(m.Value, n.Value) : null;
public static MVec4D? Outer(MVec4D? m, double? n) => m.HasValue && n.HasValue ? (MVec4D?) Outer(m.Value, n.Value) : null;
public static MVec4D? Outer(double? m, MVec4D? n) => n.HasValue && m.HasValue ? (MVec4D?) Outer(m.Value, n.Value) : null;
#endregion
#region Operators
public static MVec4D operator +(MVec4D m, MVec4D n) => Add(m, n);
public static MVec4D operator +(double c, MVec4D n) => Add(c, n);
public static MVec4D operator +(MVec4D m, double c) => Add(m, c);
public static MVec4D operator -(MVec4D m, MVec4D n) => Sub(m, n);
public static MVec4D operator -(double c, MVec4D n) => Sub(c, n);
public static MVec4D operator -(MVec4D m, double c) => Sub(m, c);
public static MVec4D operator *(MVec4D m, MVec4D n) => Mul(m, n);
public static MVec4D operator *(double c, MVec4D n) => Mul(c, n);
public static MVec4D operator *(MVec4D m, double c) => Mul(m, c);
public static MVec4D? operator /(MVec4D m, MVec4D n) => Div(m, n);
public static MVec4D? operator /(double c, MVec4D n) => Div(c, n);
public static MVec4D operator /(MVec4D m, double c) => Div(m, c);
public static MVec4D operator &(MVec4D m, MVec4D n) => Inner(m, n);
public static MVec4D operator &(MVec4D m, double c) => Inner(m, c);
public static MVec4D operator &(double c, MVec4D n) => Inner(c, n);
public static MVec4D operator ^(MVec4D m, MVec4D n) => Outer(m, n);
public static MVec4D operator ^(MVec4D m, double c) => Outer(m, c);
public static MVec4D operator ^(double c, MVec4D n) => Outer(c, n);
public static MVec4D? operator +(MVec4D? m, MVec4D? n) => Add(m, n);
public static MVec4D? operator +(double? c, MVec4D? n) => Add(c, n);
public static MVec4D? operator +(MVec4D? m, double? c) => Add(m, c);
public static MVec4D? operator -(MVec4D? m, MVec4D? n) => Sub(m, n);
public static MVec4D? operator -(double? c, MVec4D? n) => Sub(c, n);
public static MVec4D? operator -(MVec4D? m, double? c) => Sub(m, c);
public static MVec4D? operator *(MVec4D? m, MVec4D? n) => Mul(m, n);
public static MVec4D? operator *(double? c, MVec4D? n) => Mul(c, n);
public static MVec4D? operator *(MVec4D? m, double? c) => Mul(m, c);
public static MVec4D? operator /(MVec4D? m, MVec4D? n) => Div(m, n);
public static MVec4D? operator /(double? c, MVec4D? n) => Div(c, n);
public static MVec4D? operator /(MVec4D? m, double? c) => Div(m, c);
public static MVec4D? operator &(MVec4D? m, MVec4D? n) => Inner(m, n);
public static MVec4D? operator &(MVec4D? m, double? c) => Inner(m, c);
public static MVec4D? operator &(double? c, MVec4D? n) => Inner(c, n);
public static MVec4D? operator ^(MVec4D? m, MVec4D? n) => Outer(m, n);
public static MVec4D? operator ^(MVec4D? m, double? c) => Outer(m, c);
public static MVec4D? operator ^(double? c, MVec4D? n) => Outer(c, n);
public static MVec4D operator -(MVec4D m) => m.Neg;
public static MVec4D? operator ~(MVec4D m) => m.Inv;
public static MVec4D operator !(MVec4D m) => m.Rev;
public static implicit operator MVec4D(double v) => Vec0(v);
public static implicit operator MVec4D(Vector3d v) => Vec1(v.X, v.Y, v.Z, 0);
public static implicit operator MVec4D(Vector4d v) => Vec1(v.X, v.Y, v.Z, v.W);
#endregion
#region Equality

4
Tetrahedrons/TetrahedronWindow.cs
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@@ -255,14 +255,14 @@ namespace Tetrahedrons
if (Keyboard[Key.Left])
{
var rot = MVec3D.Complex(-e.Time, MVec3D.Unit12);
var rot = MVec3D.Rotor(-e.Time, MVec3D.Unit12);
_b1 = rot * _b1 * ~rot; // todo make blade classes
_b2 = rot * _b2 * ~rot;
}
if (Keyboard[Key.Right])
{
var rot = MVec3D.Complex(e.Time, MVec3D.Unit12);
var rot = MVec3D.Rotor(e.Time, MVec3D.Unit12);
_b1 = rot * _b1 * ~rot;
_b2 = rot * _b2 * ~rot;
}