第4关：视口变换与三视图

一. 任务描述

1. 本关任务

(1) 理解投影变换的方法; (2) 将main函数中的空白部分补充完整。

2. 输入

(1) 代码将自动输入一个边长为1的obj正方体模型，具体模型如下图：

(2) 代码自动将模型投影到二维平面，经过模型变换，生成一个长宽高不等的立方体，并将显示窗口一分为四，分为四个视口，每个视口大小均为原窗口大小的一半。红绿两线为四个视口的分隔线； (3) 在第一视口ViewPort中，首先将立方体沿Z轴向XOY平面投影。然后进行视口变换ViewPort，并绘制出一个白色矩形； (4) 在第二视口ViewPort1中，首先将立方体沿X轴向YOZ平面投影。然后沿Y轴顺时针旋转90度，最后进行视口变换ViewPort1，绘制一个绿色矩形； (5) 在第三视口ViewPort2中，首先将立方体沿Y轴向XOZ平面投影。然后沿X轴逆时针旋转90度，最后进行视口变换ViewPort2，绘制一个红矩形； (6) 在第四视口ViewPort3中，首先将立方体沿Y轴顺时针旋转45度，然后进行投影变换，投影变换参数eye和center已给出。最后进行视口变换ViewPort3，绘制一个黄色立方体。

3. 输出

具体结果如下图所示：

二. 相关知识

1. 投影变换

投影变换相关知识点，请参考教材与课件或有关资料。

三. 操作说明

(1) 按要求补全代码； (2) 点击窗口右下角"测评"按钮，等待测评结果，如果通过后可进行下一关任务。

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开始你的任务吧，祝你成功！

四.实验代码

#include <vector>
#include <cmath>
#include <algorithm>
#include <iostream>
#include "model.h"
#include "geometry.h"
#include "pngimage.h"
using namespace std;
const double PI = acos(-1.0);
void line(Vec3i p0, Vec3i p1, PNGImage  &image, PNGColor color)
{bool steep = false;if (std::abs(p0.x - p1.x) < std::abs(p0.y - p1.y)){std::swap(p0.x, p0.y);std::swap(p1.x, p1.y);steep = true;}if (p0.x > p1.x){std::swap(p0.x, p1.x);std::swap(p0.y, p1.y);}int dx = p1.x - p0.x;int dy = std::abs(p1.y - p0.y);int y = p0.y;int d = -dx;for (int x = p0.x; x <= p1.x; x++){if (steep)image.set(y, x, color);elseimage.set(x, y, color);d = d + 2 * dy;if (d > 0){y += (p1.y > p0.y ? 1 : -1);d = d - 2 * dx;}}
}
Matrix projection(Vec3f eye, Vec3f center)
{Matrix m = Matrix::identity(4);m[3][2] = -1.f / (eye - center).norm();return m;
}
Matrix viewport(int x, int y, int w, int h, int depth) {Matrix m = Matrix::identity(4);m[0][3] = x + w / 2.f;m[1][3] = y + h / 2.f;m[2][3] = depth / 2.f;m[0][0] = w / 2.f;m[1][1] = h / 2.f;m[2][2] = depth / 2.f;return m;
}
Matrix lookat(Vec3f eye, Vec3f center, Vec3f up) {Vec3f z = (eye - center).normalize();Vec3f x = (up^z).normalize();Vec3f y = (z^x).normalize();Matrix res = Matrix::identity(4);for (int i = 0; i < 3; i++) {res[0][i] = x[i];res[1][i] = y[i];res[2][i] = z[i];res[i][3] = -center[i];}return res;
}
Matrix translation(Vec3f v) {Matrix Tr = Matrix::identity(4);Tr[0][3] = v.x;Tr[1][3] = v.y;Tr[2][3] = v.z;return Tr;
}
Matrix scale(float factorX, float factorY, float factorZ)
{Matrix Z = Matrix::identity(4);Z[0][0] = factorX;Z[1][1] = factorY;Z[2][2] = factorZ;return Z;
}
Matrix rotation_x(float angle)
{angle = angle * PI / 180;float sinangle = sin(angle);float cosangle = cos(angle);Matrix R = Matrix::identity(4);R[1][1] = R[2][2] = cosangle;R[1][2] = -sinangle;R[2][1] = sinangle;return R;
}
Matrix rotation_y(float angle)
{angle = angle * PI / 180;float sinangle = sin(angle);float cosangle = cos(angle);Matrix R = Matrix::identity(4);R[0][0] = R[2][2] = cosangle;R[0][2] = sinangle;R[2][0] = -sinangle;return R;
}
Matrix rotation_z(float angle) {angle = angle * PI / 180;float sinangle = sin(angle);float cosangle = cos(angle);Matrix R = Matrix::identity(4);R[0][0] = R[1][1] = cosangle;R[0][1] = -sinangle;R[1][0] = sinangle;return R;
}
int main(int argc, char** argv)
{const PNGColor white = PNGColor(255, 255, 255, 255);const PNGColor black = PNGColor(0, 0, 0, 255);const PNGColor red = PNGColor(255, 0, 0, 255);const PNGColor green = PNGColor(0, 255, 0, 255);const PNGColor blue = PNGColor(0, 0, 255, 255);const PNGColor yellow = PNGColor(255, 255, 0, 255);Model *model = NULL;const int width = 800;const int height = 800;const int depth = 255;//generate some imagePNGImage image(width, height, PNGImage::RGBA); //Error when RGB because lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size() in encodeimage.init(black);model = new Model("cube.obj");Vec3f eye(0, 0, 4);Vec3f center(0, 0, 0);//添加视口变量及正投影变量代码区域/********** Begin ********/Matrix projectionMatrix = projection(eye, center);//正投影变量Matrix ViewPort = viewport(0, width/2, width/2, height/2, depth);//视口变量Matrix ViewPort1 = viewport(width / 2, width/2, width/2 , height/2 , depth);Matrix ViewPort2 = viewport(0,0 , width / 2, height / 2, depth);Matrix ViewPort3 = viewport(width / 2, 0, width / 2, height / 2, depth);/************End**********/// 绘制视口分隔线Vec3f x1(0.f, height / 2, 0.f), x2(width, height / 2, 0.f);Vec3f y1(width / 2, 0.f, 0.f), y2(width / 2, height, 0.f);line(x1, x2, image, red);line(y1, y2, image, green);for (int i = 0; i < model->nfaces(); i++){std::vector<int> face = model->face(i);for (int j = 0; j < (int)face.size(); j++){Vec3f wp0 = model->vert(face[j]);Vec3f wp1 = model->vert(face[(j + 1) % face.size()]);Matrix S0 = scale(0.5, 0.4, 0.3);Vec3f swp0 = S0 * wp0;Vec3f swp1 = S0 * wp1;//添加绘制点及绘制计算区域/********** Begin ********/Matrix ProjectionX = Matrix::identity(4);ProjectionX[0][0]=0.0f;Matrix ProjectionY = Matrix::identity(4);ProjectionY[1][1]=0.0f;Matrix ProjectionZ = Matrix::identity(4);ProjectionZ[2][2]=0.0f;Vec3f p0 = ViewPort*ProjectionZ* swp0;Vec3f p1 = ViewPort*ProjectionZ* swp1;line(p0,p1,image,white);//白色矩形Matrix R = rotation_y(90);Vec3f p0_44 = ViewPort1*R*ProjectionX* swp0;Vec3f p1_44 = ViewPort1*R*ProjectionX* swp1;line(p0_44,p1_44,image,green);//绿色矩形Matrix R1 = rotation_x(-90);Vec3f p0_55 = ViewPort2*R1*ProjectionY* swp0;Vec3f p1_55 = ViewPort2*R1*ProjectionY* swp1;line(p0_55,p1_55,image,red);//红色矩形Matrix R2 = rotation_y(45);Matrix ModelView = lookat(eye, center, Vec3f(0,-1 ,0 ));//投影变换Vec3f p0_66 = ViewPort3*ModelView*projectionMatrix*R2* swp0;Vec3f p1_66 = ViewPort3*ModelView*projectionMatrix*R2* swp1;line(p0_66,p1_66,image,yellow);//黄色立方体/************End**********/}}image.flip_vertically(); // i want to have the origin at the left bottom corner of the imageimage.write_png_file("../img_step4/test.png");delete model;return 0;
}