第3关:视口变换
一. 任务描述
1. 本关任务
(1) 理解视口变换的方法; (3) 根据视口变换的方法将viewport函数中的空白部分补充完整,并将main函数中的参数补充完整。
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) 视口矩阵中参数x、y的大小为宽度(width)的四分之一,参数w的大小为宽度的一半(width),参数h的大小为高度的一半(height),参数d=255。
3. 输出
具体结果如下图所示:
二. 相关知识
1.视口矩阵
将立方体[-1,1] * [-1,1] * [-1,1]映射到屏幕,得到立方体[x,x+w]* [y,y+h]* [0,d]。 这里d是z-buffer的分辨率,等于255,这样可以简单地转储z-buffer的黑白图像以便调试。 视口矩阵如下:
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。
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);
else
image.set(x, y, color);
d = d + 2 * dy;
if (d > 0)
{
y += (p1.y > p0.y ? 1 : -1);
d = d - 2 * dx;
}
}
}
Matrix viewport(int x, int y, int w, int h, int depth) {
Matrix m = Matrix::identity(4);
// Please add the code here
/********** Begin ********/
m[0][0]= w / 4.0 ;
m[0][3]= w / 4.0 + x;
m[1][1]= h / 4.0 ;
m[1][3]= h / 4.0 + y;
m[2][2]= depth / 2.0;
m[2][3]= depth / 2.0;
/********** End **********/
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;
Vec3f eye(0, 1.5, 4);
Vec3f center(0, 0, 0);
Matrix ModelView = lookat(eye, center, Vec3f(0, 1, 0));
Matrix Projection = Matrix::projection(eye, center);
const int width = 500;
const int height = 500;
const int depth = 255;
// Please add the code here
/********** Begin ********/
Matrix ViewPort = Matrix::viewport(width / 4, width / 4, width / 2, height / 2, depth);
/********** End **********/
//generate some image
PNGImage image(width, height, PNGImage::RGBA); //Error when RGB because lodepng_get_raw_size_lct(w, h, colortype, bitdepth) > in.size() in encode
image.init(black);
model = new Model("cube.obj");
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, 0.5, 0.5);
Vec3f swp0 = S0 * wp0;
Vec3f swp1 = S0 * wp1;
Vec3f sp0 = ViewPort*Projection*ModelView*swp0;
Vec3f sp1 = ViewPort*Projection*ModelView*swp1;
line(sp0, sp1, image, red);
}
}
image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
image.write_png_file("../img_step3/test.png");
delete model;
return 0;
}