public static Mat4 LookAt(Vect3 eye, Vect3 target, Vect3 up)
{
var vector31 = (eye - target).Normalize();
var right = up.CrossProduct(vector31).Normalize();
var vector32 = vector31.CrossProduct(right).Normalize();
return(new Mat4(new[, ]
{
{ right.X, right.Y, right.Z, 0.0 },
{ vector32.X, vector32.Y, vector32.Z, 0.0 },
{ vector31.X, vector31.Y, vector31.Z, 0.0 },
{ 0.0, 0.0, 0.0, 1.0 }
}) * Translate(-eye));
}
public static Camera CreateCamera(Vect3 position, Vect3 viewPaneCenter, Vect3 camUp, double viewPaneWidth,
double viewPaneHeight)
{
var viewPaneHeightVector = camUp;
viewPaneHeightVector *= -viewPaneHeight;
Vect3 temp1 = position - viewPaneCenter;
Vect3 viewPaneWidthVector = temp1.CrossProduct(viewPaneHeightVector);
viewPaneWidthVector = viewPaneWidthVector.Normalize();
viewPaneWidthVector *= viewPaneWidth;
viewPaneWidthVector.CopyDataTo(ref temp1);
temp1 = temp1 / 2;
Vect3 viewPaneEdge = viewPaneCenter - temp1;
viewPaneHeightVector.CopyDataTo(ref temp1);
temp1 = temp1 / 2;
viewPaneEdge -= temp1;
return(new Camera(position, viewPaneEdge, viewPaneWidthVector, viewPaneHeightVector));
}
public static double GetHitPointRayTriangleDistance(Vect3 rayPosition, Vect3 rayDirection, Vect3 trianglePos,
Vect3 triangleVect1, Vect3 triangleVect2)
{
Vect3 tmp = triangleVect1.CrossProduct(triangleVect2);
double ret = RayPlane.GetHitPointRayPlaneDistance(rayPosition, rayDirection, trianglePos, tmp);
if (double.IsPositiveInfinity(ret) || ret < Constants.EPS)
{
return(double.PositiveInfinity);
}
tmp = rayPosition + rayDirection * ret;
tmp -= trianglePos;
double uu = triangleVect1 * triangleVect1;
double uv = triangleVect1 * triangleVect2;
double vv = triangleVect2 * triangleVect2;
double wu = triangleVect1 * tmp;
double wv = triangleVect2 * tmp;
double d = uv * uv - uu * vv;
double s = (uv * wv - vv * wu) / d;
if (s < -TriEPS || s > 1 + TriEPS)
{
return(double.PositiveInfinity);
}
double t = (uv * wu - uu * wv) / d;
if (t < -TriEPS || s + t > 1 + TriEPS)
{
return(double.PositiveInfinity);
}
return(ret);
}
public static Vect3 GetCircumScribedCircleCenter(Vect3 a, Vect3 b, Vect3 c)
{
Vect3 mab = b - a;
Vect3 mac = c - a;
Vect3 normal = mab.CrossProduct(mac);
Vect3 dab = mab.CrossProduct(normal);
Vect3 dac = mac.CrossProduct(normal);
mab = a + mab / 2;
mac = a + mac / 2;
dab = dab.Normalize();
dac = dac.Normalize();
if (System.Math.Abs(dac.X) > Constants.EPS &&
System.Math.Abs(dac.Y) > Constants.EPS &&
System.Math.Abs(dab.X / dac.X - dab.Y / dac.Y) > Constants.EPS)
{
double x = ((mab.Y - mac.Y) / dac.Y - (mab.X - mac.X) / dac.X) / (dab.X / dac.X - dab.Y / dac.Y);
return(mab + dab * x);
}
if (System.Math.Abs(dac.X) > Constants.EPS &&
System.Math.Abs(dac.Z) > Constants.EPS &&
System.Math.Abs(dab.Z / dac.Z - dab.X / dac.X) > Constants.EPS)
{
double x = ((mab.X - mac.X) / dac.X - (mab.Z - mac.Z) / dac.Z) / (dab.Z / dac.Z - dab.X / dac.X);
return(mab + dab * x);
}
if (System.Math.Abs(dac.Y) > Constants.EPS &&
System.Math.Abs(dac.Z) > Constants.EPS &&
System.Math.Abs(dab.Y / dac.Y - dab.Z / dac.Z) > Constants.EPS)
{
double x = ((mab.Z - mac.Z) / dac.Z - (mab.Y - mac.Y) / dac.Y) / (dab.Y / dac.Y - dab.Z / dac.Z);
return(mab + dab * x);
}
if (System.Math.Abs(dab.Y) > Constants.EPS &&
System.Math.Abs(dab.X) > Constants.EPS &&
System.Math.Abs(dac.X / dab.X - dac.Y / dab.Y) > Constants.EPS)
{
double y = ((mac.Y - mab.Y) / dab.Y - (mac.X - mab.X) / dab.X) / (dac.X / dab.X - dac.Y / dab.Y);
return(mac + dac * y);
}
if (System.Math.Abs(dab.Z) > Constants.EPS &&
System.Math.Abs(dab.X) > Constants.EPS &&
System.Math.Abs(dac.Z / dab.Z - dac.X / dab.X) > Constants.EPS)
{
double y = ((mac.X - mab.X) / dab.X - (mac.Z - mab.Z) / dab.Z) / (dac.Z / dab.Z - dac.X / dab.X);
return(mac + dac * y);
}
if (System.Math.Abs(dab.Z) > Constants.EPS &&
System.Math.Abs(dab.Y) > Constants.EPS &&
System.Math.Abs(dac.Y / dab.Y - dac.Z / dab.Z) > Constants.EPS)
{
double y = ((mac.Z - mab.Z) / dab.Z - (mac.Y - mab.Y) / dab.Y) / (dac.Y / dab.Y - dac.Z / dab.Z);
return(mac + dac * y);
}
throw new Exception("implement more cases...");
}
public static Mat4 LookAt(Vect3 eye, Vect3 target, Vect3 up)
{
var vector31 = (eye - target).Normalize();
var right = up.CrossProduct(vector31).Normalize();
var vector32 = vector31.CrossProduct(right).Normalize();
return new Mat4(new[,]
{
{right.X, right.Y, right.Z, 0.0},
{vector32.X, vector32.Y, vector32.Z, 0.0},
{vector31.X, vector31.Y, vector31.Z, 0.0},
{0.0, 0.0, 0.0, 1.0}
}) * Translate(-eye);
}