// 123.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"
#if def__APPLE__
#include<GLUT/glut.h>
#else
#include<GL/glut.h>
#endif
#include<cmath>
#include<vector>
#include<iostream>
#include<set>
using namespace std;
set <pair<int,int>>edgeMarks;
void resize
(GLsizei w,GLsizei h
){
if
(h==0
){
h=1;
}
glViewport
(0,0,w,h
);
glMatrixMode
(GL_PROJECTION
);
glLoadIdentity
();
if
(w<=h
){
glOrtho
(0.0f,200.0f,0.0f,200.f*h/w,1.0f,-1.0f
);
}else{
glOrtho
(0.0f,200.0f*w/h,0.0f,200.0f,1.0f,-1.0f
);
}
glMatrixMode
(GL_MODELVIEW
);
glLoadIdentity
();
}
void drawPixel
(int x,int y
){
glBegin
(GL_POINTS
);
glVertex2i
(x,y
);
glEnd
();
}
//check判断
(x1,y1
)是否是三点之中的
极值点
bool check
(int x0,int y0,int x1,int y1,int x2,int y2
){
//x1是否在中间？
if
(x1>=x0&&x1>=x2
){
return false;
}
if
(x1<=x0&&x1<=x2
){
return false;
}
if
(y0>y1&&y2>y1
){
return true;
}
if
(y0<y1&&y2<y1
){
return true;
}
return false;
}
//BresenhamLine
void BresenhamLine
(vector <int>p0,vector <int>p1
){
int x0=p0[0],y0=p0[1],
x1=p1[0],y1=p1[1];
//两种特殊情况:x0==x1||y0==y1
if
(x0==x1
){
if
(y0>y1
){
swap
(y0,y1
);
}
for
(int i=y0;i<=y1;i++
){
drawPixel
(x0,i
);
}
return;
}
else if
(y0==y1
){
drawPixel
(x0,y0
);
drawPixel
(x1,y1
);
edgeMarks.insert
(make_pair
(x0,y0
));
edgeMarks.insert
(make_pair
(x1,y1
));
return;
}
int kRev=
(y1-y0
)/(x1-x0
);
bool isKGT1=false;//1:Kisgreaterthan1
bool isKNeg=
(y1-y0
)*
(x1-x0
)>=0
?false:true;//1:Kisnegative
if
(abs
(kRev
)>=1
){//|k|>1
swap
(x0,y0
);
swap
(x1,y1
);
isKGT1=true;
}
if
(isKGT1
){
if
(isKNeg
){
if
(y0<y1
){
swap
(y0,y1
);
swap
(x0,x1
);
}
}else{
if
(y0>y1
){
swap
(y0,y1
);
swap
(x0,x1
);
}
}
}else{
if
(x0>x1
){
swap
(y0,y1
);
swap
(x0,x1
);
}
}
int x=x0,y=y0;
int dx=x1-x0,dy=y1-y0;
if
(isKNeg
){
dy=-dy;
}
int e=-dx;
while
(x<=x1
){
if
(isKGT1
){
drawPixel
(y,x
);
edgeMarks.insert
(make_pair
(y,x
));
}else{
drawPixel
(x,y
);
edgeMarks.insert
(make_pair
(x,y
));
}
x++;
e+=2*dy;
if
(e>0
){
if
(isKNeg
){
y--;
}else{
y++;
}
e-=2*dx;
}
}
}
void edgeMarkFilling
(vector<vector<int>>points
){
//gety_min&y_max
int y_min=points[0][1],y_max=points[0][1];
int x_min=points[0][0],x_max=points[0][0];
//drawlines
for
(unsigned int i=1;i<points.size
();i++
){
BresenhamLine
(points[i-1],points[i]
);
y_min=min
(points[i][1],y_min
);
y_max=max
(points[i][1],y_max
);
x_min=min
(points[i][0],x_min
);
x_max=max
(points[i][0],x_max
);
//局部最低点——0个重叠的
交点，局部最高点——0个
if
(i<points.size
()-1
){
if
(check
(points[i-1][0],points[i-1][1],points[i][0],points[i][1],points[i+1][0],points[i+1][1]
)){
edgeMarks.erase
(make_pair
(points[i][0],points[i][1]
));
}
}
}
BresenhamLine
(points[0],points[points.size
()-1]
);
int lastpoint=points.size
()-1;
if
(check
(points[lastpoint-1][0],points[lastpoint-1][1],points[lastpoint][0],points[lastpoint][1],points[0][0],points[0][1]
)){
edgeMarks.erase
(make_pair
(points[lastpoint][0],points[lastpoint][1]
));
}
if
(check
(points[lastpoint][0],points[lastpoint][1],points[0][0],points[0][1],points[1][0],points[1][1]
)){
edgeMarks.erase
(make_pair
(points[0][0],points[0][1]
));
}
//filling
glColor3f
(0.0,0.0,1.0
);
glBegin
(GL_POINTS
);
for
(int i=y_max;i>=y_min;i--
){
bool isInside=false;
for
(int j=x_min;j<x_max;j++
){
if
(edgeMarks.count
(make_pair
(j,i
))==1
){
isInside=!isInside;
}
if
(isInside
){
glVertex2i
(j,i
);
//cout<<j<<''<<i<<endl;
}
}
}
glEnd
();
}
void display
(){
glClear
(GL_COLOR_BUFFER_BIT
);
glColor3d
(1,0,0
);
vector<vector<int>>points
(3
);
vector<int>p0
(2
),p1
(2
),p2
(2
),p3
(2
),p4
(2
),p5
(2
),p6
(2
);
p0[0]=40,p0[1]=40;
p1[0]=10,p1[1]=10;
p2[0]=70,p2[1]=10;
points[0]=p0;
points[1]=p1;
points[2]=p2;
edgeMarkFilling
(points
);
glutSwapBuffers
();
}
int main
(int argc,char*argv[]
){
glutInit
(&argc,argv
);
glutInitWindowSize
(400,400
);
glutInitWindowPosition
(10,10
);
glutInitDisplayMode
(GLUT_RGB|GLUT_DOUBLE
);
glutCreateWindow
("EdgeMarkFilling"
);
glutReshapeFunc
(resize
);
glutDisplayFunc
(display
);
//setRC
glClearColor
(1,1,1,1
);
glutMainLoop
();
return 0;
}
这段代码呢，总结一下遇到的问题和感想
本文通过数学论证和直观解释，揭示了一个有趣的现象：连续函数f(x)的导数f'(x)与f(x)/x相交之处正是f(x)/x取到极值的地方。进而推广到经济学中，边际成本曲线与平均成本曲线相交于后者的最低点。
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