Ejemplo n.º 1
0
        public static Point ProjectOnSegment(this Point pnt, Point segStart, Point segEnd)
        {
            Contract.Ensures((pnt - Contract.Result<Point>()).LengthSquared <= (pnt - segStart).LengthSquared);
            Contract.Ensures((pnt - Contract.Result<Point>()).LengthSquared <= (pnt - segEnd).LengthSquared);

            var v = segEnd - segStart;
            if (v.LengthSquared <= double.Epsilon) // segment is of length almost zero. Therefore any point is valid.
                return segStart;

            var u = pnt - segStart;
            var t = (u * v) / (v * v);

            if (t < 0)           // to the "left" of segStart
                return segStart;
            else if (t > 1)      // to the "right" of segEnd
                return segEnd;
            else                 // between segStart and segEnd
            {
                // the point segStart + t * v is still considered a candidate because of a numerical error that can occur
                // in the computation of "t". So we still need to choose the point with minimal distance to "pnt".
                // We do it to ensure the contract above is correct - that is, we find the closest point to "pnt" on the segment.
                var candidate = segStart + t * v;

                var potentialResults = new Tuple<Point, double>[]
                {
                    Tuple.Create(candidate, (candidate - pnt).LengthSquared),
                    Tuple.Create(segStart, (segStart - pnt).LengthSquared),
                    Tuple.Create(segEnd, (segEnd - pnt).LengthSquared),
                };

                return potentialResults.Minimizer(x => x.Item2).Item1;
            }
        }