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【计算机图形学】裁剪算法（Cohen-Sutherland算法 & 中值分割算法 & Liang-Barsky算法）_试用liang-barsky算法裁剪如图所示线段

作者：AllinToyou | 2024-05-31 12:24:30

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试用liang-barsky算法裁剪如图所示线段

一实验目的

编写直线段、多边形裁剪算法
熟悉Cohen-Sutherland算法、中值分割算法和Liang-Barsky算法的裁剪

二实验算法理论分析
Cohen-Sutherland算法：

中值分割算法：

与CS算法一样，首先对直线段端点进行编码，并把线段与窗口的关系一样分为3种情况：全在、完全不在、线段和窗口有交点，并对前两种情况进行一样的处理。对于第3种情况，则用中点分割的方法简单地把线段等分为两段，对两段重复上述测试处理，直至每条线段完全在窗口内和完全在窗口外。

可行性分析：计算机屏幕是有限的，比如1024×768个像素，x方向是2的10次方。所以这样一直二分下去的话，最多分10次。分到第十次的时候，就到像素级了，就不用再分了。所以最多循环10次。

Liang-Barsky算法：

三实验内容

1：用Cohen-Sutherland算法实现直线段裁剪

实验结果如下图所示：
第一步：依次输入A点的横坐标和纵坐标、B点的横坐标和纵坐标（此处以【0，0】为A点坐标，【400，400】为B点坐标为例）。

第二步：用户勾选需要裁剪的红色框，并将存在于矩形框内的AB线段用白色部分展示出来（此处以用户第一次点击为矩形框的左下位置，第二次点击为矩形框的右上位置为例）。

裁剪前：

裁剪后：

2：用中值分割算法实现直线段裁剪

实验结果如下图所示：
第一步：依次输入A点的横坐标和纵坐标、B点的横坐标和纵坐标（此处以【0，0】为A点坐标，【400，400】为B点坐标为例）。

裁剪前：

裁剪后：

3：用Liang-Barsky算法实现直线段裁剪

实验结果如下图所示：
第一步：依次输入A点的横坐标和纵坐标、B点的横坐标和纵坐标（此处以【0，0】为A点坐标，【400，250】为B点坐标为例）。

裁剪前：

裁剪后：

四程序说明

Project中程序的调用：

将当前cpp文件的属性——常规——从生成中排除中选择否，其他文件选择是，即可运行当前的cpp文件

1题

// 程序名称：CS裁剪

// 功能：用Cohen-Sutherland算法实现直线段裁剪

// 编译环境：VS2019，EasyX_20220116

// 最后修改：2022-3-17

#include <graphics.h>

#include <conio.h>

#include <iostream>

using namespace std;

#define LEFT 1

#define RIGHT 2

#define BOTTOM 4

#define TOP 8

int XL, XR, YB, YT;

int encode(float x, float y, int* code) {

int c = 0;

if (x < XL) {

c = c | LEFT;

}

else if (x > XR) {

c = c | RIGHT;

}

if (y < YB) {

c = c | BOTTOM;;

}

else if (y > YT) {

c = c | TOP;

}

*code = c;

return 0;

}

int CSLineClip(float x1, float y1, float x2, float y2) {

int code1, code2, code;

float x, y;

encode(x1, y1, &code1);

encode(x2, y2, &code2);

while (code1 != 0 || code2 != 0) {

if ((code1 & code2) != 0) {

return 0;

}

code = code1;

if (code1 == 0) {

code = code2;

}

if ((LEFT & code) != 0) {

x = XL;

y = y1 + (y2 - y1) * (XL - x1) / (x2 - x1);

}

else if ((RIGHT & code) != 0) {

x = XR;

y = y1 + (y2 - y1) * (XR - x1) / (x2 - x1);

}

else if ((BOTTOM & code) != 0) {

y = YB;

x = x1 + (x2 - x1) * (YB - y1) / (y2 - y1);

}

else if ((TOP & code) != 0) {

y = YT;

x = x1 + (x2 - x1) * (YT - y1) / (y2 - y1);

}

if (code == code1) {

x1 = x;

y1 = y;

encode(x, y, &code1);

}

else {

x2 = x;

y2 = y;

encode(x, y, &code2);

}

setlinecolor(WHITE);

line(x1, y1, x2, y2);

return 0;

}

int main() {

//用户定义a、b坐标

float xa, ya, xb, yb;

cout << "please input the coordinate of A point:" << endl;

cin >> xa >> ya;

cout << "please input the coordinate of B point:" << endl;

cin >> xb >> yb;

int x0, y0, x1, y1;

//0->left bottom; 1->right top;

//图形界面

initgraph(640, 480);

ExMessage m;

//勾勒AB线段：绿色

setlinecolor(GREEN);

line(xa, ya, xb, yb);

while (true) {

m = getmessage(EX_MOUSE | EX_KEY);

switch (m.message) {

case WM_LBUTTONDOWN:

x0 = m.x;

y0 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

case WM_RBUTTONDOWN:

x1 = m.x;

y1 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

//判断用户是左上~右下 / 左下~右上 / 右上~左下 / 右下~左上

if ((x0 < x1) && (y0 > y1)) {

XL = x0;

XR = x1;

YB = y1;

YT = y0;

}

else if ((x0 < x1) && (y0 < y1)) {

XL = x0;

XR = x1;

YB = y0;

YT = y1;

}

else if ((x0 > x1) && (y0 > y1)) {

XL = x1;

XR = x0;

YB = y1;

YT = y0;

}

else if ((x0 > x1) && (y0 < y1)) {

XL = x1;

XR = x0;

YB = y0;

YT = y1;

}

//勾勒裁剪框

setlinecolor(RED);

line(XL, YT, XR, YT);

line(XL, YB, XR, YB);

line(XL, YT, XL, YB);

line(XR, YT, XR, YB);

//裁剪部分为白色

CSLineClip(xa, ya, xb, yb);

case WM_KEYDOWN:

if (m.vkcode == VK_ESCAPE)

return 0; // 按 ESC 键退出程序

}

closegraph();

return 0;

}

2题

// 程序名称：中值裁剪

// 功能：用中值分割算法实现直线段裁剪

// 编译环境：VS2019，EasyX_20220116

// 最后修改：2022-3-26

// Special Thanks To Gong WH

#include <graphics.h>

#include <conio.h>

#include <iostream>

using namespace std;

#define LEFT 1

#define RIGHT 2

#define BOTTOM 4

#define TOP 8

int XL, XR, YB, YT;

//区域编码

int encode(float x, float y, int* code) {

int c = 0;

if (x < XL) {

c = c | LEFT;

}

else if (x > XR) {

c = c | RIGHT;

}

if (y < YB) {

c = c | BOTTOM;;

}

else if (y > YT) {

c = c | TOP;

}

*code = c;

return 0;

}

void MidClip(float x1, float y1, float x2, float y2) {

int code1, code2;

encode(x1, y1, &code1);

encode(x2, y2, &code2);

//无法继续二分

if (abs(x1 - x2) + abs(y1 - y2) <= 2) {

return;

}

//线段完全不可见

if ((code1 & code2) != 0) {

return;

}

//线段完全可见

if ((code1 | code2) == 0) {

setlinecolor(WHITE);

line(x1, y1, x2, y2);

return;

}

//线段部分可见=>递归吧。。

int midx = (x1 + x2) / 2, midy = (y1 + y2) / 2;

MidClip(midx, midy, x2, y2);

MidClip(x1, y1, midx, midy);

//这个优化，不大行

int midcode;

encode(midx, midy, &midcode);

//中点可见，继续二分

if (midcode == 0) {

MidClip(midx, midy, x2, y2);

MidClip(x1, y1, midx, midy);

}

//中点不可见，判断中点和哪个点在同一区域

else {

int cnt1[4] = { 0 }, cnt2[4] = { 0 }, cntmid[4] = { 0 };

//handle midcode

do {

if (midcode >= 8) {

cntmid[0] = 1;

midcode -= 8;

}

else if (midcode >= 4) {

cntmid[1] = 1;

midcode -= 4;

}

else if (midcode >= 2) {

cntmid[2] = 1;

midcode -= 2;

}

else if (midcode >= 1) {

cntmid[3] = 1;

midcode -= 1;

}

else {

continue;

}

} while (midcode != 0);

//handle code1

do {

if (code1 >= 8) {

cnt1[0] = 1;

code1 -= 8;

}

else if (code1 >= 4) {

cnt1[1] = 1;

code1 -= 4;

}

else if (code1 >= 2) {

cnt1[2] = 1;

code1 -= 2;

}

else if (code1 >= 1) {

cnt1[3] = 1;

code1 -= 1;

}

else {

continue;

}

} while (code1 != 0);

//handle code2

do {

if (code2 >= 8) {

cnt2[0] = 1;

code2 -= 8;

}

else if (code2 >= 4) {

cnt2[1] = 1;

code2 -= 4;

}

else if (code2 >= 2) {

cnt2[2] = 1;

code2 -= 2;

}

else if (code2 >= 1) {

cnt2[3] = 1;

code2 -= 1;

}

else {

continue;

}

} while (code2 != 0);

int count1 = 0, count2 = 0;

for (int i = 0; i < 4; i++) {

if (cnt1[i] == cntmid[i]) {

count1++;

}

if (cnt2[i] == cntmid[i]) {

count2++;

}

if (count1 > count2) {

//point 1 area is closer to midpoint area

MidClip(x1, y1, midx, midy);

}

else {

//point 2 area is closer to midpoint area

MidClip(midx, midy, x2, y2);

}

int main() {

//用户定义a、b坐标

int xa, ya, xb, yb;

cout << "please input the coordinate of A point:" << endl;

cin >> xa >> ya;

cout << "please input the coordinate of B point:" << endl;

cin >> xb >> yb;

int x0, y0, x1, y1;

//0->left bottom; 1->right top;

//图形界面

initgraph(640, 480);

ExMessage m;

//勾勒AB线段：绿色

setlinecolor(GREEN);

line(xa, ya, xb, yb);

while (true) {

m = getmessage(EX_MOUSE | EX_KEY);

switch (m.message) {

case WM_LBUTTONDOWN:

x0 = m.x;

y0 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

case WM_RBUTTONDOWN:

x1 = m.x;

y1 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

//判断用户是左上~右下 / 左下~右上 / 右上~左下 / 右下~左上

if ((x0 < x1) && (y0 > y1)) {

XL = x0;

XR = x1;

YB = y1;

YT = y0;

}

else if ((x0 < x1) && (y0 < y1)) {

XL = x0;

XR = x1;

YB = y0;

YT = y1;

}

else if ((x0 > x1) && (y0 > y1)) {

XL = x1;

XR = x0;

YB = y1;

YT = y0;

}

else if ((x0 > x1) && (y0 < y1)) {

XL = x1;

XR = x0;

YB = y0;

YT = y1;

}

//勾勒裁剪框

setlinecolor(RED);

line(XL, YT, XR, YT);

line(XL, YB, XR, YB);

line(XL, YT, XL, YB);

line(XR, YT, XR, YB);

//裁剪部分为白色

MidClip(xa, ya, xb, yb);

case WM_KEYDOWN:

if (m.vkcode == VK_ESCAPE)

return 0; // 按 ESC 键退出程序

}

closegraph();

return 0;

}

3题

// 程序名称：LB裁剪

// 功能：用Liang-Barsky算法实现直线段裁剪

// 编译环境：VS2019，EasyX_20220116

// 最后修改：2022-3-17

#include <graphics.h>

#include <conio.h>

#include <iostream>

using namespace std;

float XL, XR, YT, YB;

void Displayline(float x1, float y1, float x2, float y2) {

setlinecolor(WHITE);

line(x1, y1, x2, y2);

}

void LiangBarsky(float x1, float y1, float x2, float y2, float XL, float XR, float YT, float YB) {

float ansx1, ansx2, ansy1, ansy2;

//平行于y轴

if (x1 - x2 == 0) {

if (x1<XL || x1>XR) {

return;

}

else {

int ymin = max(YB, min(y1, y2));

int ymax = min(YT, max(y1, y2));

if (ymin <= ymax) {

ansx1 = ansx2 = x1;

ansy1 = ymin;

ansy2 = ymax;

}

else {

return;

}

//平行于x轴

else if (y1 - y2 == 0) {

if (y1<YB || y1>YT) {

return;

}

else {

int xmin = max(XL, min(x1, x2));

int xmax = min(XR, max(x1, x2));

if (xmin <= xmax) {

ansy1 = ansy2 = y1;

ansx1 = xmin;

ansx2 = xmax;

}

else {

return;

}

//不平行于坐标轴

else {

float p1, p2, p3, p4;

float q1, q2, q3, q4;

p1 = -(x2 - x1);

p2 = -p1;

p3 = -(y2 - y1);

p4 = -p3;

q1 = x1 - XL;

q2 = XR - x1;

q3 = y1 - YB;

q4 = YT - y1;

float u1, u2, u3, u4;

u1 = q1 / p1;

u2 = q2 / p2;

u3 = q3 / p3;

u4 = q4 / p4;

float umin, umax;

if (p1 < 0) {

if (p3 < 0) {

umin = max(0, max(u1, u3));

umax = min(1, min(u2, u4));

}

else {

umin = max(0, max(u1, u4));

umax = min(1, min(u2, u3));

}

else {

if (p3 < 0) {

umin = max(0, max(u2, u3));

umax = min(1, min(u1, u4));

}

else {

umin = max(0, max(u2, u4));

umax = min(1, min(u1, u3));

}

if (umin <= umax) {

ansx1 = x1 + umin * (x2 - x1);

ansx2 = x1 + umax * (x2 - x1);

ansy1 = y1 + umin * (y2 - y1);

ansy2 = y1 + umax * (y2 - y1);

}

else {

return;

}

Displayline(ansx1, ansy1, ansx2, ansy2);

return;

}

int main() {

//用户定义a、b坐标

float xa, ya, xb, yb;

cout << "please input the coordinate of A point:" << endl;

cin >> xa >> ya;

cout << "please input the coordinate of B point:" << endl;

cin >> xb >> yb;

float x0, y0, x1, y1;

//0->left bottom; 1->right top;

initgraph(640,480);

ExMessage m;

//勾勒AB线段：绿色

setlinecolor(GREEN);

line(xa, ya, xb, yb);

while (true) {

m = getmessage(EX_MOUSE | EX_KEY);

switch (m.message) {

case WM_LBUTTONDOWN:

x0 = m.x;

y0 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

case WM_RBUTTONDOWN:

x1 = m.x;

y1 = m.y;

setlinecolor(WHITE);

setfillcolor(GREEN);

fillrectangle(m.x - 3, m.y - 3, m.x + 3, m.y + 3);

//判断用户是左上~右下 / 左下~右上 / 右上~左下 / 右下~左上

if ((x0 < x1) && (y0 > y1)) {

XL = x0;

XR = x1;

YB = y1;

YT = y0;

}

else if ((x0 < x1) && (y0 < y1)) {

XL = x0;

XR = x1;

YB = y0;

YT = y1;

}

else if ((x0 > x1) && (y0 > y1)) {

XL = x1;

XR = x0;

YB = y1;

YT = y0;

}

else if ((x0 > x1) && (y0 < y1)) {

XL = x1;

XR = x0;

YB = y0;

YT = y1;

}

//勾勒裁剪框

setlinecolor(RED);

line(XL, YT, XR, YT);

line(XL, YB, XR, YB);

line(XL, YT, XL, YB);

line(XR, YT, XR, YB);

//裁剪部分为白色

LiangBarsky(xa, ya, xb, yb, XL, XR, YT, YB);

case WM_KEYDOWN:

if (m.vkcode == VK_ESCAPE)

return 0; // 按 ESC 键退出程序

}

closegraph(); //关闭绘图窗口

return 0;

}

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