aistudio-wpf-diagram/AIStudio.Wpf.DiagramDesigner/Helpers/SegmentHelper.cs

using System;
using System.Collections.Generic;
using System.Text;
using System.Windows;
using System.Windows.Media;

namespace AIStudio.Wpf.DiagramDesigner
{
    public class SegmentHelper
    {
        /// <summary>
        /// 获得贝塞尔曲线
        /// </summary>
        /// <param name="currentPt">当前点</param>
        /// <param name="lastPt">上一个点</param>
        /// <param name="nextPt1">下一个点1</param>
        /// <param name="nextPt2">下一个点2</param>
        /// <returns></returns>
        public static BezierSegment GetBezierSegment(Point currentPt, Point lastPt, Point nextPt1, Point nextPt2)
        {
            //计算中点
            var lastC = GetCenterPoint(lastPt, currentPt);
            var nextC1 = GetCenterPoint(currentPt, nextPt1); //贝塞尔控制点
            var nextC2 = GetCenterPoint(nextPt1, nextPt2);

            //计算相邻中点连线跟目的点的垂足
            //效果并不算太好，因为可能点在两个线上或者线的延长线上，计算会有误差
            //所以就直接使用中点平移方法。
            //var C1 = GetFootPoint(lastC, nextC1, currentPt);
            //var C2 = GetFootPoint(nextC1, nextC2, nextPt1);


            //计算“相邻中点”的中点
            var c1 = GetCenterPoint(lastC, nextC1);
            var c2 = GetCenterPoint(nextC1, nextC2);


            //计算【"中点"的中点】需要的点位移
            var controlPtOffset1 = currentPt - c1;
            var controlPtOffset2 = nextPt1 - c2;

            //移动控制点
            var controlPt1 = nextC1 + controlPtOffset1;
            var controlPt2 = nextC1 + controlPtOffset2;

            //如果觉得曲线幅度太大，可以将控制点向当前点靠近一定的系数。
            controlPt1 = controlPt1 + 0 * (currentPt - controlPt1);
            controlPt2 = controlPt2 + 0 * (nextPt1 - controlPt2);

            var bzs = new BezierSegment(controlPt1, controlPt2, nextPt1, true);
            return bzs;
        }

        /// <summary>
        ///     过c点做A和B连线的垂足
        /// </summary>
        /// <param name="aPoint"></param>
        /// <param name="bPoint"></param>
        /// <param name="cPoint"></param>
        /// <returns></returns>
        private static Point GetFootPoint(Point aPoint, Point bPoint, Point cPoint)
        {
            //设三点坐标是A，B，C，AB构成直线，C是线外的点
            //三点对边距离是a,b,c,垂足为D，
            //根据距离推导公式得：AD距离是（b平方-a平方+c平方）/2c
            //本人数学不好，可能没考虑点c在线ab上的情况
            var offsetADist = (Math.Pow(cPoint.X - aPoint.X, 2) + Math.Pow(cPoint.Y - aPoint.Y, 2) - Math.Pow(bPoint.X - cPoint.X, 2) - Math.Pow(bPoint.Y - cPoint.Y, 2) + Math.Pow(aPoint.X - bPoint.X, 2) + Math.Pow(aPoint.Y - bPoint.Y, 2)) / (2 * GetDistance(aPoint, bPoint));

            var v = bPoint - aPoint;
            var distab = GetDistance(aPoint, bPoint);
            var offsetVector = v * offsetADist / distab;
            return aPoint + offsetVector;
        }

        private static Point GetCenterPoint(Point pt1, Point pt2)
        {
            return new Point((pt1.X + pt2.X) / 2, (pt1.Y + pt2.Y) / 2);
        }

        private static double GetDistance(Point pt1, Point pt2)
        {
            return Math.Sqrt(Math.Pow(pt1.X - pt2.X, 2) + Math.Pow(pt1.Y - pt2.Y, 2));
        }
    }
}