头歌计算机图形学实验—图形几何变换和模型观察和视口变换

程序员李知恩

1393人浏览 · 2023-10-23 10:41:51

程序员李知恩 · 2023-10-23 10:41:51 发布

1. 平移、缩放、旋转正方体

#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);
	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 translation(Vec3f v) {
	Matrix Tr = Matrix::identity(4);
    // Please add the code here
    /********** Begin ********/

Tr[0][3] = v[0];
    Tr[1][3] = v[1]; 
    Tr[2][3] = v[2];
    /********** End *********/
	return Tr;
}

Matrix scale(float factorX, float factorY, float factorZ)
{
	Matrix Z = Matrix::identity(4);
    /********** Begin ********/

 Z[0][0] = factorX;
    Z[1][1] = factorY;
    Z[2][2] = factorZ;
    /********** End *********/
	return Z;
}

Matrix rotation_x(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);
	Matrix R = Matrix::identity(4);
    /********** Begin ********/
R[1][1] = cosangle;
  R[1][2] = -sinangle;
  R[2][1] = sinangle;
  R[2][2] = cosangle;

    /********** End *********/
	return R;
}

Matrix rotation_y(float angle)
{
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
    /********** Begin ********/

   R[0][0] = cosangle;
   R[0][2] = sinangle;
    R[2][0] = -sinangle;
   R[2][2] = cosangle;
    /********** End *********/
	return R;
}

Matrix rotation_z(float angle) {
	angle = angle * PI / 180;
	float sinangle = sin(angle);
	float cosangle = cos(angle);

	Matrix R = Matrix::identity(4);
    /********** Begin ********/
    R[0][0] = cosangle; 
    R[0][1] = -sinangle;
    R[1][0] = sinangle;
    R[1][1] = cosangle;

    /********** End *********/
	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 = 500;
	const int height = 500;
	const int depth = 255;

	//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("../step3/cube.obj");
	Matrix VP = viewport(width / 4, width / 4, width / 2, height / 2, depth);

	{ // draw the axes
		Vec3f x(1.f, 0.f, 0.f), y(0.f, 1.f, 0.f), o(0.f, 0.f, 0.f);
		o = VP*o;
		x = VP*x;
		y = VP*y;
		line(o, x, image, red);
		line(o, y, 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()]);
       
			// draw the original model
			Vec3f op0 = VP*wp0;
			Vec3f op1 = VP*wp1;
			line(op0, op1, image, white);

			// draw the translated model
            // Please add the code here
            /********** Begin ********/
			Matrix T = translation(Vec3f( 0.5 ,0.5  ,0.5   ));
            /********** End *********/
			Vec3f tp0 = VP*T*wp0;
			Vec3f tp1 = VP*T*wp1;
			line(tp0, tp1, image, red);

			// draw the scaled model
            // Please add the code here
            /********** Begin ********/            
			Matrix S = scale( 0.5 , 0.5 , 0.5 );
            /********** End *********/
			Vec3f sp0 = VP*S*wp0;
			Vec3f sp1 = VP*S*wp1;
			line(sp0, sp1, image, green);

			// draw the rotated model
            // Please add the code here
            /********** Begin ********/   
			Matrix R = rotation_z(45 );
            /********** End *********/
			Vec3f rp0 = VP*R*wp0;
			Vec3f rp1 = VP*R*wp1;
			line(rp0, rp1, image, yellow);
		}
	}
	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;
}

2. 图形的平移与缩放

#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);
	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 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 = 500;
    const int height = 500;
    const int depth = 255;
    //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");
    Matrix VP = viewport(width / 4, width / 4, width / 2, height / 2, depth);
    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;
            // draw the model after scaled
            Vec3f op0 = VP * swp0;
            Vec3f op1 = VP * swp1;
            line(op0, op1, image, white);
            Matrix T = translation(Vec3f(0.5, 0.5, 0.5));
            Matrix S = scale(0.5, 0.5, 0.5);
            // scaled then translated
            Vec3f tsp0 = VP*T*S*swp0;
            Vec3f tsp1 = VP*T*S*swp1;
            line(tsp0, tsp1, image, red);
            // translated then scaled
            Vec3f stp0 = VP*S*T*swp0;
            Vec3f stp1 = VP*S*T*swp1;
            line(stp0, stp1, image, green);
        }
    }
    image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
    image.write_png_file("../img_step2/test.png");
    delete model;
    return 0;
}

3.图形的平移与旋转

#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);
	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 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 = 500;
    const int height = 500;
    const int depth = 255;
    //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");
    Matrix VP = viewport(width / 4, width / 4, width / 2, height / 2, depth);
    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;
            // draw the model after scaled
            Vec3f op0 = VP * swp0;
            Vec3f op1 = VP * swp1;
            line(op0, op1, image, white);
            Matrix T = translation(Vec3f(0.5, 0.5, 0.5));
            Matrix S = scale(0.5, 0.5, 0.5);
            Matrix R = rotation_z(45);
            // translated then rotated
            Vec3f rtp0 = VP*R*T*swp0;
            Vec3f rtp1 = VP*R*T*swp1;
            line(rtp0, rtp1, image, green);
            // rotated then translated
            Vec3f trp0 = VP*T*R*swp0;
            Vec3f trp1 = VP*T*R*swp1;
            line(trp0, trp1, image, red);
        }
    }
    image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
    image.write_png_file("../img_step1/test.png");
    delete model;
    return 0;
}

4图形的旋转与缩放

#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);
	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 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 = 500;
    const int height = 500;
    const int depth = 255;
    //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");
    Matrix VP = viewport(width / 4, width / 4, width / 2, height / 2, depth);
    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;
            // draw the model after scaled
            Vec3f op0 = VP * swp0;
            Vec3f op1 = VP * swp1;
            line(op0, op1, image, white);
            Matrix T = translation(Vec3f(0.5, 0.5, 0.5));
            Matrix S = scale(1, 0.5, 0.5);
            Matrix R = rotation_z(45);
            // scaled then rotated
            Vec3f rsp0 = VP*R*S*swp0;
            Vec3f rsp1 = VP*R*S*swp1;
            line(rsp0, rsp1, image, green);
            // rotated then scaled
            Vec3f srp0 = VP*S*R*swp0;
            Vec3f srp1 = VP*S*R*swp1;
            line(srp0, srp1, image, red);
        }
    }
    image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
    image.write_png_file("../img_step4/test.png");
    delete model;
    return 0;
}

5. 绘制三菱形状

#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);
	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 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 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");
    Matrix VP = viewport(width / 4, width / 4, width / 2, height / 2, depth);
    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;
            Matrix S = scale(1, 0.5, 0.5);
            Matrix R1 = rotation_z(45);
            Matrix T = translation(Vec3f(sqrt(2)/2, 0, 0));
            Matrix R2 = rotation_z(90);
            // 中间坚直的菱形
            Vec3f mp0 = VP*R2*T*S*R1*swp0;
            Vec3f mp1 = VP*R2*T*S*R1*swp1;
            line(mp0, mp1, image, red);
            // 左边的菱形
            Matrix R3 = rotation_z(120);
            Vec3f lp0 = VP * R3* R2*T*S*R1*swp0;
            Vec3f lp1 = VP * R3* R2*T*S*R1*swp1;
            line(lp0, lp1, image, green);
            // 右边的菱形
            Matrix R4 = rotation_z(-120);
            Vec3f rp0 = VP * R4* R2*T*S*R1*swp0;
            Vec3f rp1 = VP * R4* R2*T*S*R1*swp1;
            line(rp0, rp1, image, yellow);
        }
    }
    image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
    image.write_png_file("../img_step5/test.png");
    delete model;
    return 0;
}

8视口变换

#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/2;
    m[0][3]=x+(w/2);
    m[1][1]=h/2;
    m[1][3]=y+h/2;
    m[2][2]=255/2;
    m[2][3]=255/2;
    m[3][3]=1;
    
 
 
 
	/********** 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 = 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;
}

7. 观察变换

#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 lookat(Vec3f eye, Vec3f center, Vec3f up) {
    Matrix res = Matrix::identity(4);
	// Please add the code here
    /********** Begin ********/
    Vec3f z = (eye - center).normalize();
	Vec3f x = (up^z).normalize();
	Vec3f y = (z^x).normalize();
	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];
	}
 
 
	/********** End ********/
	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 = 500;
	const int height = 500;
	const int depth = 255;
 
	// Please add the code here
    /********** Begin ********/
    Vec3f eye(0 ,1.5  ,4  );
	Vec3f center( 0, 0 ,0  );
	Matrix ModelView = lookat(eye, center, Vec3f( 0, 1 ,0  ));
	// Please add the code here
    /********** Begin ********/
 
	Matrix Projection = Matrix::projection(eye, center);
	Matrix ViewPort = Matrix::viewport(width / 4, width / 4, width / 2, height / 2, depth);
 
 
	//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_step2/test.png");
	delete model;
	return 0;
}

6 模型变换

#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 translation(Vec3f v) {//平移
	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 = 500;
	const int height = 500;
	const int depth = 255;
	Vec3f eye(0.5, 1.5, 4);
	Vec3f center(0, 0, 0);
 
	Matrix Projection = Matrix::projection(eye, center);
	Matrix ViewPort = Matrix::viewport(width / 4, width / 4, width / 2, height / 2, depth);
 
 
	//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;
 
			// for comparing - draw the model after scaled 
			Vec3f op0 = ViewPort * Projection * swp0;
			Vec3f op1 = ViewPort * Projection * swp1;
			line(op0, op1, image, white);
 
			// Please add the code here
            /********** Begin ********/
 
 
            //3) 将白色立方体的顶点坐标向x轴正方向平移1.2个单位距离，然后绘制一个红色立方形
            Matrix S1 = translation(Vec3f(1.2,0.0,0.0));
 
            op0 = ViewPort * Projection *S1 * swp0;
			 op1 = ViewPort * Projection *S1 * swp1;
			line(op0, op1, image, red);
 
           
 
 
 
            // (4) 将白色立方体的顶点坐标沿y轴逆时针方向旋转30度，再向x轴负方向平移1.3个单位距离，然后绘制一个绿色正方形
        //    Matrix rotation_y(float angle)
             Matrix S3 = rotation_y(30.0);
             Matrix S4 = translation(Vec3f(-1.3,0.0,0.0));
             op0 = ViewPort * Projection *S4 *S3 * swp0;
             op1 = ViewPort * Projection *S4 *S3 * swp1;
             line(op0, op1, image,green );
            /********** End *********/
		}
	}
 
	image.flip_vertically(); // i want to have the origin at the left bottom corner of the image
	image.write_png_file("../img_step1/test.png");
	delete model;
	return 0;
}

DAMO开发者矩阵

DAMO开发者矩阵，由阿里巴巴达摩院和中国互联网协会联合发起，致力于探讨最前沿的技术趋势与应用成果，搭建高质量的交流与分享平台，推动技术创新与产业应用链接，围绕“人工智能与新型计算”构建开放共享的开发者生态。

更多推荐

Rebuild-Z × GEIA AI 黑客松全方案｜48小时具身智能创新实验，两种创业路线同台碰撞

DAMO开发者矩阵

ROS 2 参数服务（Parameter Service）从零到一实战：环境避坑与 Python 动态配置详解

文章不仅提供了解决 NO_PUBKEY、软件包无法定位等常见安装报错的避坑方案，还手把手带领读者用 Python 编写一个支持“热加载”动态修改配置的节点，带你彻底了解机器人参数配置的核心原理。它允许我们在节点运行期间，通过命令行、Launch 文件或其他节点，动态地读取和修改节点内部的参数（Key-Value 键值对），完全无需重启节点。至此，你不仅通过命令行体验了参数服务的威力，还编写了属于自

DAMO开发者矩阵

2026年第二季度中国人工智能产业发展报告：从“技术突围”到“产业深水区”

政策层面，6月堪称“AI政策月”——工信部印发《“人工智能+信息通信”创新发展实施意见》，商务部等八部门出台《关于加快“人工智能+消费”发展的实施意见》，《人工智能智能体互联》系列7项国家标准正式发布，国务院常务会议专题听取人工智能发展情况汇报并部署重点工作。这个季度，国产大模型首次跨越“生产级质变点”，国产AI芯片龙头市值突破万亿元大关，具身智能融资规模逼近2025年全年总和，中国AI研究在顶