我试图了解由cambridgesoft开发的行业领先的化学工具ChemDraw如何构建Bezier曲线,以便我可以手动将Bezier曲线点从其他程序/例程(例如自制的Delphi / C#实用程序)转换为可以识别ChemDraw的曲线数据.在开始之前,我必须承认我在询问某个黑盒子内部如何工作,因此想要为任何麻烦道歉并感谢任何帮助！
我在ChemDraw中制作了四种最简单的Bezier曲线,并将它们保存为.CDXML文件,其曲线部分最后粘贴了. .CDXML文件和相应的图片都可以从fileserve下载. Download Bezier_curve_ChemDraw_sample here. ChemDraw trial edition can be downloaded here.
问题
问题1.例如,以“线”类型的曲线点为例,我在制作此曲线时总共有两个点.为什么ChemDraw会为它存储六个积分？ ChemDraw如何准确地解释这些要点？其他三种类型存在同样的问题,最多使用四个显式点.
问题2.如果在ChemDraw中显示“Bezier曲线使用三点 – 第一类型”的内容,可以看到第一个点不能是(12.22,104.25).我的意思是,它的X坐标明显大于12.为什么会发生这种情况？ ChemDraw会对数据进行一些转换吗？ “使用四点的贝塞尔曲线”存在同样的问题.
问题3.似乎CurvePoints属性末尾的额外空白字符有所不同.有什么区别？
有人可以告诉我这些问题吗？
ChemDraw .CDXML文件中的曲线部分
============行==============
<curve id="2" Z="1" ArrowheadType="Solid" CurvePoints="143.47 116.25 143.47 116.25 143.47 116.25 300.22 117.75 300.22 117.75 300.22 117.75" />
============贝塞尔曲线使用三点 – 第一类==============
<curve id="2" Z="1" ArrowheadType="Solid" CurvePoints="12.22 104.25 121.72 106.5 231.22 108.75 230.47 204 230.47 204 230.47 204" />
============贝塞尔曲线使用三点 – 第二类==============
<curve id="2" Z="1" ArrowheadType="Solid" CurvePoints="134.47 97.5 134.47 97.5 134.47 97.5 231.22 60.75 229.72 109.5 228.22 158.25" />
============贝塞尔曲线使用四点==============
<curve id="2" Z="1" ArrowheadType="Solid" CurvePoints="5.47 93.75 123.22 93.75 240.97 93.75 351.22 177.75 236.47 177.75 121.72 177.75" />
示例C#程序生成相同的曲线
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
namespace WinForms_2_DrawBezier
{
public partial class Form1 : Form
{
public Form1()
{
InitializeComponent();
}
private void Form1_Load(object sender,EventArgs e)
{
Text = "Draw Bezier Curve";
}
private void Form1_Paint(object sender,PaintEventArgs e)
{
// DrawBezier_1(this,e);
// DrawBezier_2(this,e);
// DrawBezier_3(this,e);
DrawBezier_4(this,e);
}
private void DrawBezier_1(object sender,PaintEventArgs e)
{
Pen l_pen = new Pen(Color.Black);
PointF l_pt1 = new PointF(143.47f,116.25f);
PointF l_pt2 = new PointF(l_pt1.X,l_pt1.Y);
PointF l_pt3 = new PointF(l_pt1.X,l_pt1.Y);
PointF l_pt4 = new PointF(300.22f,117.75f);
PointF l_pt5 = new PointF(l_pt4.X,l_pt4.Y);
PointF l_pt6 = new PointF(l_pt4.X,l_pt4.Y);
PointF[] l_pts = new PointF[6];
l_pts[0] = l_pt1;
l_pts[1] = l_pt2;
l_pts[2] = l_pt3;
l_pts[3] = l_pt4;
l_pts[4] = l_pt5;
l_pts[5] = l_pt6;
// e.Graphics.DrawBezier(l_pen,l_pt1,l_pt2,l_pt5,l_pt6);
e.Graphics.DrawBezier(l_pen,l_pt3,l_pt4,l_pt6); // As suggested by Dani
// e.Graphics.DrawBeziers(l_pen,l_pts);
}
private void DrawBezier_2(object sender,PaintEventArgs e)
{
Pen l_pen = new Pen(Color.Black);
PointF l_pt1 = new PointF(12.22f,104.25f);
PointF l_pt2 = new PointF(121.72f,106.5f);
PointF l_pt3 = new PointF(231.22f,108.75f);
PointF l_pt4 = new PointF(230.47f,204f);
PointF l_pt5 = new PointF(l_pt4.X,l_pt4);
e.Graphics.DrawBezier(l_pen,l_pts);
}
private void DrawBezier_3(object sender,PaintEventArgs e)
{
Pen l_pen = new Pen(Color.Black);
PointF l_pt1 = new PointF(134.47f,97.5f);
PointF l_pt2 = new PointF(l_pt1.X,l_pt1.Y);
PointF l_pt4 = new PointF(231.22f,60.75f);
PointF l_pt5 = new PointF(229.72f,109.5f);
PointF l_pt6 = new PointF(228.22f,158.25f);
PointF[] l_pts = new PointF[6];
l_pts[0] = l_pt1;
l_pts[1] = l_pt2;
l_pts[2] = l_pt3;
l_pts[3] = l_pt4;
l_pts[4] = l_pt5;
l_pts[5] = l_pt6;
// e.Graphics.DrawBezier(l_pen,l_pts);
}
private void DrawBezier_4(object sender,PaintEventArgs e)
{
Pen l_pen = new Pen(Color.Black);
PointF l_pt1 = new PointF(5.47f,93.75f);
PointF l_pt2 = new PointF(123.22f,93.75f);
PointF l_pt3 = new PointF(240.97f,93.75f);
PointF l_pt4 = new PointF(351.22f,177.75f);
PointF l_pt5 = new PointF(236.47f,177.75f);
PointF l_pt6 = new PointF(121.72f,177.75f);
PointF[] l_pts = new PointF[6];
l_pts[0] = l_pt1;
l_pts[1] = l_pt2;
l_pts[2] = l_pt3;
l_pts[3] = l_pt4;
l_pts[4] = l_pt5;
l_pts[5] = l_pt6;
// e.Graphics.DrawBezier(l_pen,l_pts);
}
}
}
解决方法
它使用标准贝塞尔曲线算法,可以采用任意数量的点来构建曲线.看看
Bézier curve
编辑：
C#DrawBezier仅支持二次(四点)贝塞尔曲线.您将使用以下四点贝塞尔曲线转换为C#：
float[] CurvePoints = GetCurvePoints(); DrawBezier(Pen,CurvePoints[0],CurvePoints[1],CurvePoints[4],CurvePoints[5],CurvePoints[6],CurvePoints[7],CurvePoints[10],CurvePoints[11]);
GetCurvePoints()只是为您提供CurvePoints xml属性中的点列表.
编辑2：
代码重现最后一条曲线的所有曲线：
using System;
using System.Drawing;
using System.Windows.Forms;
using System.Linq;
using System.Collections.Generic;
public class Bezier : Form
{
static public void Main ()
{
Application.Run (new Bezier ());
}
protected override void OnPaint (PaintEventArgs e)
{
// The input with all points
string CurveDataString = "5.47 93.75 123.22 93.75 240.97 93.75 351.22 177.75 236.47 177.75 121.72 177.75";
string[] CurveDataStringParts = CurveDataString.Split(' ');
int[] Keep = {2,3,4,5,6,7,8,9};
float[] CurveData = (from i in Keep select float.Parse(CurveDataStringParts[i])).ToArray();
e.Graphics.DrawBezier(Pens.Black,CurveData[0],CurveData[1],CurveData[2],CurveData[3],CurveData[4],CurveData[5],CurveData[6],CurveData[7]);
for(int i = 0; i < CurveData.Length; i += 2)
{
e.Graphics.FillEllipse(Brushes.Black,new RectangleF(CurveData[i] - 2,CurveData[i + 1] - 2,4));
}
base.OnPaint (e);
}
}
结果：
