Exemplo n.º 1
0
        /*
         * There are some not obvious calculations.
         * With them we can find the closest points of 
         * two straits. Function returns mean point of 
         * them.
         * p11, p21 - some points of straits.
         * p12, p22 - some other points of straits.
         * a1, a2 - vectors of straits.
         */

        public static Line3D GetPerpendicular(Line3D line1, Line3D line2)
        {
            Point3D p11 = line1.Begin;
            Point3D p21 = line2.Begin;
            Point3D a1 = line1.Direction.Normalize();
            Point3D a2 = line2.Direction.Normalize();

            if (Math.Abs(a1.X - a2.X) < Epsilon && Math.Abs(a1.Y - a2.Y) < Epsilon &&
                Math.Abs(a1.Z - a2.Z) < Epsilon)
                throw new Exception("straits are parallel");

            var p12 = new Point3D(p11.X + a1.X, p11.Y + a1.Y, p11.Z + a1.Z);
            var p22 = new Point3D(p21.X + a2.X, p21.Y + a2.Y, p21.Z + a2.Z);

            double p1 = (p12.X - p11.X)*(p12.X - p11.X) + (p12.Y - p11.Y)*(p12.Y - p11.Y) +
                        (p12.Z - p11.Z)*(p12.Z - p11.Z);
            double p2 = (p12.X - p11.X)*(p22.X - p21.X) + (p12.Y - p11.Y)*(p22.Y - p21.Y) +
                        (p12.Z - p11.Z)*(p22.Z - p21.Z);
            double q1 =
                -((p22.X - p21.X)*(p12.X - p11.X) + (p22.Y - p21.Y)*(p12.Y - p11.Y) + (p22.Z - p21.Z)*(p12.Z - p11.Z));
            double q2 =
                -((p22.X - p21.X)*(p22.X - p21.X) + (p22.Y - p21.Y)*(p22.Y - p21.Y) + (p22.Z - p21.Z)*(p22.Z - p21.Z));
            double r1 = (p21.X - p11.X)*(p12.X - p11.X) + (p21.Y - p11.Y)*(p12.Y - p11.Y) +
                        (p21.Z - p11.Z)*(p12.Z - p11.Z);
            double r2 = (p21.X - p11.X)*(p22.X - p21.X) + (p21.Y - p11.Y)*(p22.Y - p21.Y) +
                        (p21.Z - p11.Z)*(p22.Z - p21.Z);

            double m = (q2*r1 - q1*r2)/(p1*q2 - p2*q1);
            double n = (p1*r2 - p2*r1)/(p1*q2 - p2*q1);

            double x1 = p11.X + m*(p12.X - p11.X);
            double y1 = p11.Y + m*(p12.Y - p11.Y);
            double z1 = p11.Z + m*(p12.Z - p11.Z);

            double x2 = p21.X + n*(p22.X - p21.X);
            double y2 = p21.Y + n*(p22.Y - p21.Y);
            double z2 = p21.Z + n*(p22.Z - p21.Z);

            return new Line3D(new Point3D(x1, y1, z1), new Point3D(x2, y2, z2));
        }
Exemplo n.º 2
0
 public Line3D Apply(Line3D arg)
 {
     return(new Line3D(Apply(arg.Begin), Apply(arg.End)));
 }
Exemplo n.º 3
0
 public static double Distance(Point3D point, Line3D line)
 {
     Point3D vector = point - line.Begin;
     return vector.MultiplyVector(line.Direction).Norm()/line.Direction.Norm();
 }
Exemplo n.º 4
0
 public static bool IsParallel(Line3D line1, Line3D line2)
 {
     return AreCollinear(line1.Direction, line2.Direction);
 }
Exemplo n.º 5
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        public static double Distance(Point3D point, Line3D line)
        {
            Point3D vector = point - line.Begin;

            return(vector.MultiplyVector(line.Direction).Norm() / line.Direction.Norm());
        }
Exemplo n.º 6
0
 public static bool IsParallel(Line3D line1, Line3D line2)
 {
     return(AreCollinear(line1.Direction, line2.Direction));
 }
Exemplo n.º 7
0
 public Line3D Apply(Line3D arg)
 {
     return new Line3D(Apply(arg.Begin), Apply(arg.End));
 }