无法绘制多边形？

Question

这里有一个 class 画星星，作为 Bjarne Stroustrup 的 C++ 编程：原理与实践.

第 13 章练习 19 的一部分

Class Star uses penta-, hexa-, hepta- and octa-gram as basis together with a property (rotational symmetry) that stars with multiple vertices (10, 12, 14, 18, etc) have, to draw n-grams¹:

Chapter13Exercise19.cpp

#include "GUI.h"
#include "Simple_window.h"
#include <iostream>
#include "Chapter13Exercise19.h"

int main(){
     // window parameters
     int winWidth = 800;
     int winHeight = 600;
     Point centerPoint((x_max() - winWidth) / 2, (y_max() - winHeight) / 2);
     Simple_window* siw = new Simple_window(centerPoint, winWidth,
                                            winHeight, "Chapter 13 Exercise 19");

 try{
     Point center(siw->x_max()/2, siw->y_max()/2);
     int radius = 150;
     // Currenly: sides > 5, sides =! 13, 17, 19 and multiples
     int sides = 16;

     Graph_lib::Star st(center, radius, sides);
     siw->attach(st);
     siw->wait_for_button();
 }catch(exception& e){
    cerr << e.what() << endl;
    getchar();
 }catch(const std::invalid_argument& e){ 
     cerr << e.what() << endl;
     getchar();
 }catch(...){
    cerr <<"Defaul exception!"<< endl;
    getchar();
 }

}

Chapter13Exercise19.h

#ifndef _Chapter13Exercise19_H_
#define _Chapter13Exercise19_H_
#define PI 3.14159265359

namespace Graph_lib{
class Star: public Lines{
public:
    Star(Point c, int r, int n);
private:
    int vertexNumber;
    Point center;
    int radius;
    vector<Point>starCoordinates;
    // parameters kept as function recursive
    void rotateCoordinate(Point& axisOfRotation, Point& initial, 
                          double angRads, int numberOfRotations);
    void generatePoly();
    void makeStar();
};
#include "Chapter13Exercise19Def.cpp"
} // end of namespace Graph_lib

#endif

Chapter13Exercise19Def.cpp

// Class Members implementation
Star::Star(Point c, int r, int n)
    : vertexNumber(n), center(c), radius(r)
{ 
    if(n < 5) throw std::invalid_argument("Not enough verteces!");
    generatePoly(); 
    makeStar();
}

void Star::rotateCoordinate(Point& axisOfRotation, Point& initial,
                            double angRads, int numberOfRotations){
    if(numberOfRotations <= 0) return;
    else{
        double x = cos(angRads) * (initial.x - axisOfRotation.x)
                 - sin(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.x;
        double y = sin(angRads) * (initial.x - axisOfRotation.x) 
                 + cos(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.y;
        starCoordinates.push_back(Point(x, y));
        rotateCoordinate(axisOfRotation, Point(x,y), angRads, --numberOfRotations);
    }
}

void Star::generatePoly(){ 
    double angRads = (PI / 180.) * (360. / vertexNumber);
    Point initial(center.x, center.y - radius);
    rotateCoordinate(center, initial, angRads, vertexNumber);
}

void Star::makeStar(){
    // every if statement covers Star with n and multiples of n vertexes
    // the inner for loops execute one iteration for the fundamental stars
    // and n iterations for the multiples (rotational symmetry)
    if (vertexNumber % 5 == 0){
        for (size_t it = 0; it < starCoordinates.size() / 5; ++it){
            Lines::add(starCoordinates[it+3], starCoordinates[it]);
            Lines::add(starCoordinates[it], starCoordinates[it+2]);
            Lines::add(starCoordinates[it+2], starCoordinates[it+4]);
            Lines::add(starCoordinates[it+4], starCoordinates[it+1]);
            Lines::add(starCoordinates[it+1], starCoordinates[it+3]);
        }
    }else if (vertexNumber % 3 == 0){
        for (size_t it = 0; it < starCoordinates.size() / 3; ++it){
            Lines::add(starCoordinates[it], starCoordinates[it+2]);
            Lines::add(starCoordinates[it+2], starCoordinates[it+4]);
            Lines::add(starCoordinates[it+4], starCoordinates[it]);
        }
    }else if (vertexNumber % 7 == 0){
        for (size_t it = 0; it < starCoordinates.size() / 7; ++it){
            Lines::add(starCoordinates[it], starCoordinates[it+3]);
            Lines::add(starCoordinates[it+3], starCoordinates[it+6]);
            Lines::add(starCoordinates[it+6], starCoordinates[it+2]);
            Lines::add(starCoordinates[it+2], starCoordinates[it+5]);
            Lines::add(starCoordinates[it+5], starCoordinates[it+1]);
            Lines::add(starCoordinates[it+1], starCoordinates[it+4]);
            Lines::add(starCoordinates[it+4], starCoordinates[it]);
        }
    }else if (vertexNumber % 8 == 0){
        for (size_t it = 0; it < starCoordinates.size() / 8; ++it){
            Lines::add(starCoordinates[it], starCoordinates[it+5]);
            Lines::add(starCoordinates[it+5], starCoordinates[it+2]);
            Lines::add(starCoordinates[it+2], starCoordinates[it+7]);
            Lines::add(starCoordinates[it+7], starCoordinates[it+4]);
            Lines::add(starCoordinates[it+4], starCoordinates[it+1]);
            Lines::add(starCoordinates[it+1], starCoordinates[it+6]);
            Lines::add(starCoordinates[it+6], starCoordinates[it+3]);
            Lines::add(starCoordinates[it+3], starCoordinates[it]);
       }
   } else throw std::invalid_argument("Star vertexes'number not supported!");
}

结果：

虽然所有基本的多边形（5、6、7、8 个顶点）看起来都应该是这样，但在多边形的顶点为：10、12、14 等的情况下，我得到了这些部分完成的图纸。

我知道问题来自 Chapter13Exercise19Def.cpp 中的函数 makeStar()，但我无法弄清楚问题是什么。

问题：

为什么来的图是画的一半，函数实现有什么问题makeStar()？
是否有其他算法可以完成类似的工作？

^{1.目前是 5、6、7 和 8 的倍数。}

可以找到所有用于编译的附加文件：here. The FLTK could be found here。

Answer 1

我真的不能玩你的代码，因为它依赖于你正在使用的可视化库，但我知道问题出在哪里，而且我非常有信心我知道解决方案。

rotateCoordinate 递归函数生成点向量，沿多边形的边界圆均匀分布，按顺时针方向排列。

当您随后构建定义（绘制...）多边形的线条时，您使用的是点，但不是用于更正索引。例如，假设您有一个多边形 {16/2}（2 个六角星），您有 0-15 个索引点，但是生成线条的 for 循环最多达到索引 8（it = 1, index [it + 7]), 这显然是错误的.

你应该做的是用你的多边形中多边形的数量乘以你的常量数（你添加到 it 的数），所以在 {16/2} 的情况下就是 2 .

试试这个代码：

void Star::makeStar(){
    // every if statement covers Star with n and multiples of n vertexes
    // the inner for loops execute one iteration for the fundamental stars
    // and n iterations for the multiples (rotational symmetry)
    if (vertexNumber % 5 == 0){
        for (size_t it = 0, polygons = starCoordinates.size() / 5; it < polygons; ++it){
            Lines::add(starCoordinates[it + polygons * 3], starCoordinates[it]);
            Lines::add(starCoordinates[it], starCoordinates[it + polygons * 2]);
            Lines::add(starCoordinates[it + polygons * 2], starCoordinates[it + polygons * 4]);
            Lines::add(starCoordinates[it + polygons * 4], starCoordinates[it + polygons * 1]);
            Lines::add(starCoordinates[it + polygons * 1], starCoordinates[it + polygons * 3]);
        }
    }else if (vertexNumber % 6 == 0){ // for polygons multiples of 6
        size_t polygons = starCoordinates.size() / 6;
        for (size_t it = 0, ; it < starCoordinates() / 3; ++it){
            // generated by two triangles 
            Lines::add(starCoordinates[it], starCoordinates[it + polygons * 2]);
            Lines::add(starCoordinates[it + polygons * 2], starCoordinates[it + polygons * 4]);
            Lines::add(starCoordinates[it + polygons * 4], starCoordinates[it]);
        }
    }else if (vertexNumber % 7 == 0){
        for (size_t it = 0, polygons = starCoordinates.size() / 7; it < polygons; ++it){
            Lines::add(starCoordinates[it], starCoordinates[it + polygons * 3]);
            Lines::add(starCoordinates[it + polygons * 3], starCoordinates[it + polygons * 6]);
            Lines::add(starCoordinates[it + polygons * 6], starCoordinates[it + polygons * 2]);
            Lines::add(starCoordinates[it + polygons * 2], starCoordinates[it + polygons * 5]);
            Lines::add(starCoordinates[it + polygons * 5], starCoordinates[it + polygons * 1]);
            Lines::add(starCoordinates[it + polygons * 1], starCoordinates[it + polygons * 4]);
            Lines::add(starCoordinates[it + polygons * 4], starCoordinates[it]);
        }
    }else if (vertexNumber % 8 == 0){
        for (size_t it = 0, polygons = starCoordinates.size() / 8; it < polygons; ++it){
            Lines::add(starCoordinates[it], starCoordinates[it + polygons * 5]);
            Lines::add(starCoordinates[it + polygons * 5], starCoordinates[it + polygons * 2]);
            Lines::add(starCoordinates[it + polygons * 2], starCoordinates[it + polygons * 7]);
            Lines::add(starCoordinates[it + polygons * 7], starCoordinates[it + polygons * 4]);
            Lines::add(starCoordinates[it + polygons * 4], starCoordinates[it + polygons * 1]);
            Lines::add(starCoordinates[it + polygons * 1], starCoordinates[it + polygons * 6]);
            Lines::add(starCoordinates[it + polygons * 6], starCoordinates[it + polygons * 3]);
            Lines::add(starCoordinates[it + polygons * 3], starCoordinates[it]);
       }
   } else throw std::invalid_argument("Star vertexes'number not supported!");
}

无法绘制多边形？

Failing to draw polygrams?

c++

algorithm

computational-geometry

结果：

问题：