33、插入一段大学学的计算机，正儿八经的计算机图形学

public void breasenCircle(int a,int b,int r) {
int x0 = 0;
int y0 = r;
int y = y0;
int x = x0;
GL.Vertex2(x + a, y + b);
double p = y * y - 2 * (r * r - (x + 1) * (x + 1)) + (y - 1) * (y - 1);
while(x<=x0+(Math.Sqrt(2)/2)*r){
if (p > 0)
{
p = p + 4 * (x - y) + 10;
x = x + 1;
y = y - 1;
GL.Vertex2(x+a, y+b);
GL.Vertex2(y+a, x+b);
GL.Vertex2(x+a,-y+b);
GL.Vertex2(-y+a,x+b);
GL.Vertex2(-x+a,-y+b);
GL.Vertex2(-y+a,-x+b);
GL.Vertex2(-x+a, y+b);
GL.Vertex2(y+a, -x+b);
}
else
{

p = p + 4 * x + 6;
x = x + 1;
GL.Vertex2(x+a, y+b);
GL.Vertex2(y+a, x+b);
GL.Vertex2(x+a, -y+b);
GL.Vertex2(-y+a, x+b);
GL.Vertex2(-x+a, -y+b);
GL.Vertex2(-y+a, -x+b);
GL.Vertex2(-x+a, y+b);
GL.Vertex2(y+a, -x+b);
}

}
}

public void Bresenhamline(int x0, int y0, int x1, int y1) {
double dx = x1 - x0;
double dy = y1 - y0;
int x=x0;
int y=y0;
double b = (y0 * x1 - y1 * x0) / (x1 - x0);
if (Math.Abs(dy / dx) <= 1)
{
double p = 2 * dx * y - 2 * dy * x - 2 * dy - 2 * b * dx + dx;
while (Math.Abs(x1 - x) > 1)
{
if (p > 0)
{
x = x + 1;
GL.Vertex2(x, y);
p = p - 2 * dy;
}
else
{
x = x + 1;
y = y + 1;
p = p + 2 * dx - 2 * dy;
GL.Vertex2(x, y);
}
}
}
else {
double p = 2 * x * dy - 2 * dx * y + dy - 2 * dx + 2 * dx * b;
while (Math.Abs(y1 - y) > 1) {
if (p > 0)
{
y = y + 1;
GL.Vertex2(x, y);
p = p - 2 * dx;
}
else {
x = x + 1;
y = y + 1;
GL.Vertex2(x,y);
p = p + 2 * dy - 2 * dx;
}
}

}

}

public void midLine(int x0,int y0,int x1,int y1) {
double a = y0 - y1;
double b = x1 - x0;
int x = x0;
int y = y0;
GL.Vertex2(x,y);
if (Math.Abs(a / b) < 1)
{
double d = 2 * a + b;
while (x < x1)
{
if (d < 0)
{
x = x + 1;
y = y + 1;
GL.Vertex2(x, y);
d = d + a + b;
}
else
{
x = x + 1;
GL.Vertex2(x, y);
d = d + 2 * a;
}
}
}
else {
double d = a + 2 * b;
while(y<y1){
if (d < 0)
{
y = y + 1;
GL.Vertex2(x, y);
d = d + 2 * b;
}
else
{
y = y + 1;
x = x + 1;
GL.Vertex2(x,y);
d = d + 2 * a + 2 * b;
}
}
}
}

public void DDALine(int x0,int y0,int x1,int y1) {
float dx, dy, y, k,x;
dx = x1 - x0; dy = y1 - y0;
k = dy / dx; y = y0; x = x0;
if (k <= 1)
{
for (x = x0; x < x1; x++)
{
GL.Vertex2(x, Math.Floor(y + 0.5));
y = y + k;
}
}
else {
for (y = y0; y < y1; y++)
{
GL.Vertex2(Math.Floor(x + 0.5), y);
x = x + 1 / k;
}
}

}

private void glControl1_Paint(object sender, PaintEventArgs e)
{
if (!loaded)
return;
GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadIdentity();
GL.Color3(Color.Green);
GL.Begin(BeginMode.Polygon);
GL.Vertex2(1, 1);
GL.Vertex2(20, 80);
GL.Vertex2(30, 200);
GL.Vertex2(50, 180);
GL.Vertex2(60, 50);
GL.End();
allPaint8(50, 160, Color.Green, Color.Red);
//paintGraphy();
GL.End();
glControl1.SwapBuffers();
}
//八联通递归填充算法
public void allPaint8(int x, int y, Color boundry, Color fillColor)
{

if (Getpixel(x, y).ToArgb() != fillColor.ToArgb() && Getpixel(x, y).ToArgb() == boundry.ToArgb())
{

GL.Color3(fillColor);
GL.Begin(BeginMode.Points);
GL.Vertex2(x, y);
GL.End();
allPaint8(x - 1, y - 1, boundry, fillColor);
allPaint4(x, y - 1, boundry, fillColor);
allPaint8(x + 1, y - 1, boundry, fillColor);
allPaint8(x - 1, y, boundry, fillColor);
allPaint4(x + 1, y, boundry, fillColor);
allPaint4(x, y + 1, boundry, fillColor);
allPaint8(x - 1, y + 1, boundry, fillColor);
allPaint8(x + 1, y + 1, boundry, fillColor);

}

}

//四联通递归填充算法
public void allPaint4(int x,int y,Color boundry,Color fillColor) {
if (Getpixel(x, y).ToArgb()!= fillColor.ToArgb() && Getpixel(x, y).ToArgb()==boundry.ToArgb())
{

GL.Color3(fillColor);
GL.Begin(BeginMode.Points);
GL.Vertex2(x, y);
GL.End();
allPaint4(x - 1, y,boundry,fillColor);
allPaint4(x, y + 1, boundry, fillColor);
allPaint4(x + 1, y, boundry, fillColor);
allPaint4(x, y - 1, boundry, fillColor);
}

}

多边形扫描线填充：

填充之前的图像如上所示：
填充之后的图像如下所示：

private void glControl1_Paint(object sender, PaintEventArgs e)
{
if (!loaded)
return;
GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadIdentity();
GL.Color3(Color.Green);
GL.Begin(BeginMode.Points);
GL.Vertex2(1, 1);
GL.Vertex2(20, 80);
GL.Vertex2(30, 200);
GL.Vertex2(50, 180);
GL.Vertex2(60, 50);
GL.End();
paintGraphy();
GL.End();
glControl1.SwapBuffers();
}

//多边形扫描线算法
public void paintGraphy() {
NList nlist = new NList(1);
GL.Vertex2(1, 1);
GL.Vertex2(20, 80);
nlist.Add(new Node(1, (20.0 - 1.0) / (80.0 - 1.0), 80));
GL.Vertex2(30, 200);
nlist.Add(new Node(20, (30.0 - 20.0) / (200.0 - 80.0), 200));
GL.Vertex2(50, 180);
nlist.Add(new Node(50, (50.0 - 30.0) / (180.0 - 200.0), 200));
GL.Vertex2(60, 50);
nlist.Add(new Node(60, (60.0 - 50.0) / (50.0 - 180.0), 180));
nlist.Add(new Node(1, (60.0 - 1.0) / (50.0 - 1.0), 50));
double t = 0;
for (int i = 1; i <= 200; i++) {
List<Point> listPoint = new List<Point>();

for (int j = 0; j < nlist.myndL.Count; j++) {
if (j == 0) {
if (i > 1 && i <= nlist.myndL[0].ymax) {
listPoint.Add(new Point(nlist.myndL[j].x + i*nlist.myndL[0].dx, i));

}
}
else if (j == 1)
{
if (i > 1 && i <= nlist.myndL[1].ymax)
{
listPoint.Add(new Point(nlist.myndL[0].x + i*nlist.myndL[1].dx, i));

}

}
else if (j == 2) {
if (i > nlist.myndL[0].ymax && i <= nlist.myndL[j + 1].ymax) {
t = i - nlist.myndL[0].ymax;
listPoint.Add(new Point(nlist.myndL[j].x + t * nlist.myndL[j].dx, i));
}
}
else
{
double YMAX;
if (j + 1 == nlist.myndL.Count)
{
YMAX = nlist.myndL[1].ymax;
}
else {
YMAX=nlist.myndL[j + 1].ymax;
}
double valueJ_1 = Math.Min(YMAX, nlist.myndL[j].ymax);
double valueUp = Math.Max(YMAX, nlist.myndL[j].ymax);
if (i >valueJ_1 && i <= valueUp )
{
t = i - valueJ_1;
listPoint.Add(new Point(nlist.myndL[j].x + t * nlist.myndL[j].dx, i));

}
}

}
if (listPoint.Count == 2)
{
Bresenhamline(listPoint[0].x, listPoint[0].y, listPoint[1].x, listPoint[1].y);
}
}
}

1.    图形的二维旋转

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;
using OpenTK.Graphics.OpenGL;
namespace mywapp
{
public partial class Form1 : Form
{
bool loaded = false;
public Form1()
{
InitializeComponent();
}

private void glControl1_Load(object sender, EventArgs e)
{
loaded = true;
GL.ClearColor(Color.White);
SetupViewport();
}
private void SetupViewport()
{
int w = glControl1.Width;
int h = glControl1.Height;
GL.MatrixMode(MatrixMode.Projection);
GL.LoadIdentity();
GL.Ortho(0, w, 0, h, -1, 1); // Bottom-left corner pixel has coordinate (0, 0)
GL.Viewport(0, 0, w, h); // Use all of the glControl painting area
}

private void glControl1_Paint(object sender, PaintEventArgs e)
{
if (!loaded)
return;
GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadIdentity();
GL.Color3(Color.Green);
GL.Begin(BeginMode.LineLoop);
GL.Vertex2(1, 1);
GL.Vertex2(20, 80);
GL.Vertex2(30, 200);
GL.Vertex2(50, 180);
GL.Vertex2(60, 50);
List<Point> list = new List<Point>();
list.Add(new Point(1, 1));
list.Add(new Point(20,80));
list.Add(new Point(30,200));
list.Add(new Point(50, 180));
list.Add(new Point(60, 50));
List<Point> nlist = rotato2(-30, list);
foreach (Point point in nlist) {
GL.Vertex2(point.x,point.y);
}
GL.End();
glControl1.SwapBuffers();
}

//二维旋转
private List<Point> rotato2(int angel, List<Point> points)
{
double o=(angel*Math.PI)/180.0;
double[,] a = new double[,] { { Math.Cos(o), -Math.Sin(o) }, { Math.Sin(o), Math.Cos(o) } };
foreach (Point point in points) {
point.x = a[0, 0] * point.x + a[0, 1] * point.y;
point.y = a[1, 0] * point.x + a[1, 1] * point.y;
}
return points;

}

二维平移
将原图形在x轴上向右平移80个单位像素，在y轴上向上平移20个单位像素

//二维平移
private List<Point> moveLocation(int x, int y, List<Point> points) {
foreach (Point point in points)
{
point.x = point.x + x;
point.y = point.y + y;
}
return points;
}

二维缩放
将原图形放大了1.3倍之后，在x轴上向右平移了60个单位像素后，得到的图形：

//二维缩放
private List<Point> changeSize2(double size, List<Point> points) {
double[,] a = new double[,] { { size, 0 }, { 0, size } };
foreach (Point point in points)
{
point.x = a[0, 0] * point.x + a[0, 1] * point.y;
point.y = a[1, 0] * point.x + a[1, 1] * point.y;
}
return points;
}

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;
using OpenTK.Graphics.OpenGL;
namespace mywapp
{
public partial class Form1 : Form
{
bool loaded = false;
public Form1()
{
InitializeComponent();
}

private void glControl1_Load(object sender, EventArgs e)
{
loaded = true;
GL.ClearColor(Color.White);
SetupViewport();
}
private void SetupViewport()
{
int w = glControl1.Width;
int h = glControl1.Height;
GL.MatrixMode(MatrixMode.Projection);
GL.LoadIdentity();
GL.Ortho(0, w, 0, h, -1, 1); // Bottom-left corner pixel has coordinate (0, 0)
GL.Viewport(0, 0, w, h); // Use all of the glControl painting area
}

private void glControl1_Paint(object sender, PaintEventArgs e)
{
if (!loaded)
return;
GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadIdentity();
GL.Color3(Color.Green);
GL.Begin(BeginMode.Points);
GL.Vertex2(10, 30);
GL.Vertex2(40, 60);
GL.Vertex2(70, 50);
GL.Vertex2(120, 100);
GL.End();
int[,] shuzu = new int[4, 2] { { 10, 30 }, { 40, 60 }, { 70, 50 }, { 120, 110 } };
drawBezierCurve(shuzu);
glControl1.SwapBuffers();
}

//Bezier画曲线算法
public void drawBezierCurve(int[,] shuzu)
{
int n = 0;
if ((n = shuzu.GetLength(0)) < 2)
return;
for (double t = 0.0; t <= 1; t += 0.05 / n)
{
double[,] pshuzu = new double[1, 2] { { 0, 0 } };
computeP(shuzu, n - 1, t, pshuzu);
GL.Color3(Color.Red);
GL.Begin(BeginMode.Points);
GL.Vertex2(pshuzu[0, 0], pshuzu[0, 1]);
GL.End();
}
}
void computeP(int[,] pshuzu, int count, double u, double[,] p)
{
int i = 0;
int k = 0;
double[,] Pshuzu = new double[count + 1, 2];

for (i = 0; i <= count; i++)
{
Pshuzu[i, 0] = pshuzu[i, 0];
Pshuzu[i, 1] = pshuzu[i, 1];
}
for (k = 1; k <= count; k++)
{
for (i = 0; i <= count - k; i++)
{
Pshuzu[i, 0] = ((1 - u) * Pshuzu[i, 0] + u * Pshuzu[i + 1, 0]);
Pshuzu[i, 1] = ((1 - u) * Pshuzu[i, 1] + u * Pshuzu[i + 1, 1]);
}
}
p[0, 0] = Pshuzu[0, 0];
p[0, 1] = Pshuzu[0, 1];
}
}
}