public Coordinate Rotate(Coordinate coord)
{
// http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
var q = new Quaternion(coord.Normalise(), 0);
var temp = q * Conjugate();
return((this * temp).Vector);
}
public Vector(Coordinate normal, decimal distance)
: base(0, 0, 0)
{
Normal = normal.Normalise();
Distance = distance;
var temp = Normal * Distance;
X = temp.X;
Y = temp.Y;
Z = temp.Z;
}
public Plane(Coordinate norm, decimal distanceFromOrigin)
{
Normal = norm.Normalise();
DistanceFromOrigin = distanceFromOrigin;
PointOnPlane = Normal * DistanceFromOrigin;
A = Normal.X;
B = Normal.Y;
C = Normal.Z;
D = -DistanceFromOrigin;
}
public Plane(Coordinate norm, Coordinate pointOnPlane)
{
Normal = norm.Normalise();
DistanceFromOrigin = Normal.Dot(pointOnPlane);
PointOnPlane = pointOnPlane;
A = Normal.X;
B = Normal.Y;
C = Normal.Z;
D = -DistanceFromOrigin;
}
public Plane(Coordinate norm, decimal distanceFromOrigin)
{
Normal = norm.Normalise();
DistanceFromOrigin = distanceFromOrigin;
PointOnPlane = Normal * DistanceFromOrigin;
A = Normal.X;
B = Normal.Y;
C = Normal.Z;
D = -DistanceFromOrigin;
}
public Plane(Coordinate norm, Coordinate pointOnPlane)
{
Normal = norm.Normalise();
DistanceFromOrigin = Normal.Dot(pointOnPlane);
PointOnPlane = pointOnPlane;
A = Normal.X;
B = Normal.Y;
C = Normal.Z;
D = -DistanceFromOrigin;
}
public Vector(Coordinate normal, decimal distance)
: base(0, 0, 0)
{
Normal = normal.Normalise();
Distance = distance;
var temp = Normal * Distance;
X = temp.X;
Y = temp.Y;
Z = temp.Z;
}
public static Matrix Rotation(Coordinate axis, decimal angle)
{
var cos = DMath.Cos(-angle);
var sin = DMath.Sin(-angle);
var t = 1m - cos;
axis = axis.Normalise();
return(new Matrix(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0,
t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0,
t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0,
0, 0, 0, 1));
}
public static Color Tint(Coordinate sun, Coordinate normal, Color c)
{
var tintvar = (double)sun.Normalise().Dot(normal.Normalise());
// tint variation = 128
var diff = (int)(64 * (tintvar + 1));
return Color.FromArgb(c.A, Math.Max(0, c.R - diff), Math.Max(0, c.G - diff), Math.Max(0, c.B - diff));
}
public static Quaternion AxisAngle(Coordinate axis, decimal angle)
{
return(axis.VectorMagnitude() == 0
? Identity
: new Quaternion(axis.Normalise() * DMath.Sin(angle / 2), DMath.Cos(angle / 2)).Normalise());
}
public static Matrix Rotation(Coordinate axis, decimal angle)
{
var cos = DMath.Cos(-angle);
var sin = DMath.Sin(-angle);
var t = 1m - cos;
axis = axis.Normalise();
return new Matrix(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0,
t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0,
t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0,
0, 0, 0, 1);
}
public Coordinate Rotate(Coordinate coord)
{
// http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
var q = new Quaternion(coord.Normalise(), 0);
var temp = q * Conjugate();
return (this * temp).Vector;
}
public static Quaternion AxisAngle(Coordinate axis, decimal angle)
{
return axis.VectorMagnitude() == 0
? Identity
: new Quaternion(axis.Normalise() * DMath.Sin(angle / 2), DMath.Cos(angle / 2)).Normalise();
}
