C# Marching-Square算法中的插值
是源代码的存储库C# Marching-Square算法中的插值,c#,algorithm,interpolation,marching-cubes,C#,Algorithm,Interpolation,Marching Cubes,是源代码的存储库 在“线性插值”部分,本文讨论了当直线倾斜时如何插值 例如,对于案例2,其计算如下: 我实施了如下插值: public class Square { public Point A { get; set; }//bottom left point public Point B { get; set; }//bottom right point public Point C { get; set; }//top right point pub
public class Square
{
public Point A { get; set; }//bottom left point
public Point B { get; set; }//bottom right point
public Point C { get; set; }//top right point
public Point D { get; set; }//top left point
public double A_data { get; set; }//bottom left data
public double B_data { get; set; }//bottom right data
public double C_data { get; set; }//top roght data
public double D_data { get; set; }//top left data
public Square()
{
A = new Point();
B = new Point();
C = new Point();
D = new Point();
}
private double GetCaseId(double threshold)
{
int caseId = 0;
if (A_data >= threshold)
{
caseId |= 1;
}
if (B_data >= threshold)
{
caseId |= 2;
}
if (C_data >= threshold)
{
caseId |= 4;
}
if (D_data >= threshold)
{
caseId |= 8;
}
return caseId;
}
public List<Line> GetLines(double Threshold)
{
List<Line> linesList = new List<Line>();
double caseId = GetCaseId(Threshold);
if (caseId == 0) {/*do nothing*/ }
if (caseId == 15) {/*do nothing*/ }
if ((caseId == 1) || (caseId == 14))
{
double pX = B.X + (A.X - B.X) * ((1 - B_data) / (A_data - B_data));
double pY = B.Y;
Point p = new Point(pX, pY);
double qX = D.X;
double qY = D.Y + (A.Y - D.Y) * ((1 - D_data) / (A_data - D_data));
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*2==13*/
if ((caseId == 2) || (caseId == 13))//B
{
double pX = A.X + (B.X - A.X) * ((1 - A_data) / (B_data - A_data));
double pY = A.Y;
Point p = new Point(pX, pY);
double qX = C.X;
double qY = C.Y + (B.Y - C.Y) * ((1 - C_data) / (B_data - C_data));
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*3==12*/
if ((caseId == 3) || (caseId == 12))
{
double pX = A.X;
double pY = A.Y + (D.Y - A.Y) * ((1 - A_data) / (D_data - A_data));
Point p = new Point(pX, pY);
double qX = C.X;
double qY = C.Y + (B.Y - C.Y) * ((1 - C_data) / (B_data - C_data));
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*4==11*/
if ((caseId == 4) || (caseId == 11))
{
double pX = D.X + (C.X - D.X) * ((1 - D_data) / (C_data - D_data));
double pY = D.Y;
Point p = new Point(pX, pY);
double qX = B.X;
double qY = B.Y + (C.Y - B.Y) * ((1 - B_data) / (C_data - B_data));
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*6==9*/
if ((caseId == 6) || (caseId == 9))
{
double pX = A.X + (B.X - A.X) * ((1 - A_data) / (B_data - A_data));
double pY = A.Y;
Point p = new Point(pX, pY);
double qX = C.X + (D.X - C.X) * ((1 - C_data) / (D_data - C_data));
double qY = C.Y;
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*7==8*/
if ((caseId == 7) || (caseId == 8))
{
double pX = C.X + (D.X - C.X) * ((1 - C_data) / (D_data - C_data));
double pY = C.Y;
Point p = new Point(pX, pY);
double qX = A.X;
double qY = A.Y + (D.Y - A.Y) * ((1 - A_data) / (D_data - A_data));
Point q = new Point(qX, qY);
Line line = new Line(p, q);
linesList.Add(line);
}
/*ambiguous case*/
if (caseId == 5)
{
double pX1 = A.X + (B.X - A.X) * ((1 - A_data) / (B_data - A_data));
double pY1 = A.Y;
Point p1 = new Point(pX1, pY1);
double qX1 = C.X;
double qY1 = C.Y + (B.Y - C.Y) * ((1 - C_data) / (B_data - C_data));
Point q1 = new Point(qX1, qY1);
Line line1 = new Line(p1, q1);
double pX2 = C.X + (D.X - C.X) * ((1 - C_data) / (D_data - C_data));
double pY2 = C.Y;
Point p2 = new Point(pX2, pY2);
double qX2 = A.X;
double qY2 = A.Y + (D.Y - A.Y) * ((1 - A_data) / (D_data - A_data));
Point q2 = new Point(qX2, qY2);
Line line2 = new Line(p2, q2);
linesList.Add(line1);
linesList.Add(line2);
}
if (caseId == 10)
{
double pX1 = B.X + (A.X - B.X) * ((1 - B_data) / (A_data - B_data));
double pY1 = B.Y;
Point p1 = new Point(pX1, pY1);
double qX1 = D.X;
double qY1 = D.Y + (A.Y - D.Y) * ((1 - D_data) / (A_data - D_data));
Point q1 = new Point(qX1, qY1);
Line line1 = new Line(p1, q1);
double pX2 = D.X + (C.X - D.X) * ((1 - D_data) / (C_data - D_data));
double pY2 = D.Y;
Point p2 = new Point(pX2, pY2);
double qX2 = B.X;
double qY2 = B.Y + (C.Y - B.Y) * ((1 - B_data) / (C_data - B_data));
Point q2 = new Point(qX2, qY2);
Line line2 = new Line(p2, q2);
linesList.Add(line1);
linesList.Add(line2);
}
return linesList;
}
公共类广场
{
公共点A{get;set;}//左下角点
公共点B{get;set;}//右下角点
公共点C{get;set;}//右上角点
公共点D{get;set;}//左上点
公共双A_数据{get;set;}//左下角数据
公共双B_数据{get;set;}//右下角数据
公共双C_数据{get;set;}//top-roght数据
公共双D_数据{get;set;}//左上角数据
公众广场()
{
A=新点();
B=新点();
C=新点();
D=新点();
}
私有双GetCaseId(双阈值)
{
int caseId=0;
如果(A_数据>=阈值)
{
caseId |=1;
}
如果(B_数据>=阈值)
{
caseId |=2;
}
如果(C_数据>=阈值)
{
caseId |=4;
}
如果(D_数据>=阈值)
{
caseId |=8;
}
返回caseId;
}
公共列表GetLines(双阈值)
{
列表行列表=新列表();
双caseId=GetCaseId(阈值);
如果(caseId==0){/*什么也不做*/}
如果(caseId==15){/*什么也不做*/}
if((caseId==1)| |(caseId==14))
{
双pX=B.X+(A.X-B.X)*((1-B_数据)/(A_数据-B_数据));
双pY=B.Y;
点p=新点(pX,pY);
双qX=D.X;
双qY=D.Y+(A.Y-D.Y)*((1-D_数据)/(A_数据-D_数据));
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*2==13*/
如果((caseId==2)| |(caseId==13))//B
{
双pX=A.X+(B.X-A.X)*((1-A_数据)/(B_数据-A_数据));
双pY=A.Y;
点p=新点(pX,pY);
双qX=C.X;
双qY=C.Y+(B.Y-C.Y)*((1-C_数据)/(B_数据-C_数据));
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*3==12*/
if((caseId==3)| |(caseId==12))
{
双pX=A.X;
双pY=A.Y+(D.Y-A.Y)*((1-A_数据)/(D_数据-A_数据));
点p=新点(pX,pY);
双qX=C.X;
双qY=C.Y+(B.Y-C.Y)*((1-C_数据)/(B_数据-C_数据));
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*4==11*/
if((caseId==4)| |(caseId==11))
{
双pX=D.X+(C.X-D.X)*((1-D_数据)/(C_数据-D_数据));
双pY=D.Y;
点p=新点(pX,pY);
双qX=B.X;
双qY=B.Y+(C.Y-B.Y)*((1-B_数据)/(C_数据-B_数据));
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*6==9*/
if((caseId==6)| |(caseId==9))
{
双pX=A.X+(B.X-A.X)*((1-A_数据)/(B_数据-A_数据));
双pY=A.Y;
点p=新点(pX,pY);
双qX=C.X+(D.X-C.X)*((1-C_数据)/(D_数据-C_数据));
双qY=C.Y;
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*7==8*/
if((caseId==7)| |(caseId==8))
{
双pX=C.X+(D.X-C.X)*((1-C_数据)/(D_数据-C_数据));
双pY=C.Y;
点p=新点(pX,pY);
双qX=A.X;
双qY=A.Y+(D.Y-A.Y)*((1-A_数据)/(D_数据-A_数据));
点q=新点(qX,qY);
直线=新直线(p,q);
行列表。添加(行);
}
/*暧昧案件*/
如果(caseId==5)
{
双pX1=A.X+(B.X-A.X)*((1-A_数据)/(B_数据-A_数据));
双pY1=A.Y;
点p1=新点(pX1,pY1);
双qX1=C.X;
双qY1=C.Y+(B.Y-C.Y)*((1-C_数据)/(B_数据-C_数据));
点q1=新点(qX1,qY1);
第1行=新行(p1,q1);
双pX2=C.X+(D.X-C.X)*((1-C_数据)/(D_数据-C_数据));
双pY2=C.Y;
点p2=新点(pX2,pY2);
双qX2=A.X;
双qY2=A.Y+(D.Y-A.Y)*((1-A_数据)/(D_数据-A_数据));
点q2=新点(qX2,qY2);
第2行=新行(p2,q2);
linesList.Add(第1行);
linesList.Add(第2行);
}
如果(caseId==10)
{
双pX1=B.X+(A.X-B.X)*((1-B_数据)/(A_数据-B_数据));
双pY1=B.Y;
点p1=新点(pX1,pY1);
双qX1=D.X;
双qY1=D.Y+(A.Y-D.Y)*((1-D_数据)/(A_数据-D_数据));
点q1=新点(qX1,qY1);
第1行=新行(p1,q1);
双pX2=D.X+(C.X-D.X)*((1-D_数据)/(C_数据-D_数据));
双pY2=D.Y;
点p2=新点(pX2,pY2);
双qX2=B.X;
双qY2=B.Y+(C.Y-B.Y)*((1-B_数据)/(C_数据-B_数据));
点q2=新点(qX2,qY2);
第2行=新行(p2,q2);
linesList.Add(第1行);
linesList.Add(第2行);
}
返回l
double a = Data[j + 1, i];
double b = Data[j + 1, i + 1];
double c = Data[j, i + 1];
double d = Data[j, i];
Point A = new Point(xVector[i], yVector[j + 1]);//A
Point B = new Point(xVector[i + 1], yVector[j + 1]);//B
Point C = new Point(xVector[i + 1], yVector[j]);//C
Point D = new Point(xVector[i], yVector[j]);//D
double a = Data[j, i];
double b = Data[j, i + 1];
double c = Data[j+1, i + 1];
double d = Data[j+1, i];
Point A = new Point(j, i);//A
Point B = new Point(j, i+1);//B
Point C = new Point(j+1, i+1);//C
Point D = new Point(j+1,i);//D
using System;
using System.Collections.Generic;
namespace G__Marching_Sqaure
{
public class Square
{
public Point A { get; set; } //bottom left point
public Point B { get; set; } //bottom right point
public Point C { get; set; } //top right point
public Point D { get; set; } //top left point
public double A_data { get; set; } //bottom left data
public double B_data { get; set; } //bottom right data
public double C_data { get; set; } //top roght data
public double D_data { get; set; } //top left data
public Square()
{
A = new Point();
B = new Point();
C = new Point();
D = new Point();
}
private LineShapes GetCaseId(double threshold)
{
int caseId = 0;
if (A_data >= threshold)
{
caseId |= 1;
}
if (B_data >= threshold)
{
caseId |= 2;
}
if (C_data >= threshold)
{
caseId |= 4;
}
if (D_data >= threshold)
{
caseId |= 8;
}
return (LineShapes)caseId;
}
public List<Line> GetLines(double Threshold)
{
List<Line> linesList = new List<Line>();
LineShapes caseId = GetCaseId(Threshold);
if (caseId == LineShapes.Empty)
{
/*do nothing*/
}
if (caseId == LineShapes.All)
{
/*do nothing*/
}
if ((caseId == LineShapes.BottomLeft) || (caseId == LineShapes.AllButButtomLeft))
{
var p = InterpolateHorizonal(B, A, B_data, A_data);
var q = InterpolateVertical(D, A, D_data, A_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*2==13*/
if ((caseId == LineShapes.BottomRight) || (caseId == LineShapes.AllButButtomRight)) //B
{
var p = InterpolateHorizonal(A, B, A_data, B_data);
var q = InterpolateVertical(C, B, C_data, B_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*3==12*/
if ((caseId == LineShapes.Bottom) || (caseId == LineShapes.Top))
{
// interpolate vertical
var p = InterpolateVertical(A, D, A_data, D_data);
var q = InterpolateVertical(C, B, C_data, B_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*4==11*/
if ((caseId == LineShapes.TopRight) || (caseId == LineShapes.AllButTopRight))
{
var p = InterpolateHorizonal(D, C, D_data, C_data);
var q = InterpolateVertical(B, C, B_data, C_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*6==9*/
if ((caseId == LineShapes.Right) || (caseId == LineShapes.Left))
{
var p = InterpolateHorizonal(A, B, A_data, B_data);
var q = InterpolateHorizonal(C, D, C_data, D_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*7==8*/
if ((caseId == LineShapes.AllButTopLeft) || (caseId == LineShapes.TopLeft))
{
var p = InterpolateHorizonal(C, D, C_data, D_data);
var q = InterpolateVertical(A, D, A_data, D_data);
Line line = new Line(p, q);
linesList.Add(line);
}
/*ambiguous case*/
if (caseId == LineShapes.TopRightBottomLeft)
{
var p1 = InterpolateHorizonal(A, B, A_data, B_data);
var q1 = InterpolateVertical(C, B, C_data, B_data);
Line line1 = new Line(p1, q1);
var p2 = InterpolateHorizonal(C, D, C_data, D_data);
var q2 = InterpolateVertical(A, D, A_data, D_data);
Line line2 = new Line(p2, q2);
linesList.Add(line1);
linesList.Add(line2);
}
if (caseId == LineShapes.TopLeftBottomRight)
{
var p1 = InterpolateHorizonal(B, A, B_data, A_data);
var q1 = InterpolateVertical(D, A, D_data, A_data);
Line line1 = new Line(p1, q1);
var p2 = InterpolateHorizonal(D, C, D_data, C_data);
var q2 = InterpolateVertical(B, C, B_data, C_data);
Line line2 = new Line(p2, q2);
linesList.Add(line1);
linesList.Add(line2);
}
return linesList;
}
private static Point InterpolateVertical(Point point, Point point1, double data, double data1)
{
double qX = point.X;
double qY = point.Y + (point1.Y - point.Y) * ((1 - data) / (data1 - data));
Point q = new Point(qX, qY);
return q;
}
private static Point InterpolateHorizonal(Point start, Point end, double startForce, double endForce)
{
double pX = start.X + (end.X - start.X) * ((1 - startForce) / (endForce - startForce));
double pY = start.Y;
Point p = new Point(pX, pY);
return p;
}
}
internal enum LineShapes
{
Empty = 0,
// ○----○
// | |
// | |
// ○----○
BottomLeft = 1,
// ○----○
// | |
// | |
// ●----○
BottomRight = 2,
// ○----○
// | |
// | |
// ○----●
Bottom = 3,
// ○----○
// | |
// | |
// ●----●
TopRight = 4,
// ○----●
// | |
// | |
// ○----○
TopRightBottomLeft = 5,
// ○----●
// | |
// | |
// ●----○
Right = 6,
// ○----●
// | |
// | |
// ○----●
AllButTopLeft = 7,
// ○----●
// | |
// | |
// ●----●
TopLeft = 8,
// ●----○
// | |
// | |
// ○----○
Left = 9,
// ●----○
// | |
// | |
// ●----○
TopLeftBottomRight = 10,
// ●----○
// | |
// | |
// ○----●
AllButTopRight = 11,
// ●----○
// | |
// | |
// ●----●
Top = 12,
// ●----●
// | |
// | |
// ○----○
AllButButtomRight = 13,
// ●----●
// | |
// | |
// ●----○
AllButButtomLeft = 14,
// ●----●
// | |
// | |
// ○----●
All = 15,
// ●----●
// | |
// | |
// ●----●
}
}
private static Point InterpolateVertical(Point start, Point end, double startForce, double endForce, double threshold)
{
double a = ((threshold - startForce) / (endForce - startForce));
double qX = start.X;
double qY = start.Y + (end.Y - start.Y) * a;
Point q = new Point(qX, qY);
return q;
}
private static Point InterpolateHorizonal(Point start, Point end, double startForce, double endForce, double threshold)
{
double a = ((threshold - startForce) / (endForce - startForce));
double pX = start.X + (end.X - start.X) * a;
double pY = start.Y;
Point p = new Point(pX, pY);
return p;
}
int height = 1000;
int width = height;
int resolution = 20;
double threshold = 0.9;
int xLen = width / resolution;
int yLen = height / resolution;
int[] x = new int[xLen];
int[] y = new int[yLen];
for (int i = 0; i < xLen; i++)
{
x[i] = i * resolution;
}
for (int j = 0; j < yLen; j++)
{
y[j] = j * resolution;
}
/////////////////////SIN-COS/////////////////////////////
double[,] example = new double[xLen, yLen];
for (int j = 0; j < yLen; j++)
{
for (int i = 0; i < xLen; i++)
{
double example_l = Math.Sin(i * resolution /100.0 ) * Math.Cos(j * resolution /100.0);
example[j, i] = example_l;
}
}