Sol+Bài giải bài tập Đồ họa máy tính

Solution Tut 4
Câu 1
Gọi
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
D








là ma trận của phép biến đối xứng qua trục Oy
T(0,1)R
z
(45
0
)DR
z
(-45
0
)T(0,-1)
2 2 2 2
0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0
2 2 2 2
0 1 0 1 0 1 0 0 0 1 0 1

2 2 2 2
0 0 0 0
* * * *
2 2 2 2
0 0 1 0 0 0 1 0 0 0 1 0
0 0 1 0 0 0 1 0
0 0 0 1 0 0 0 1 0 0 0 1
0 0 0 1 0 0 0 1
0 1 0 1
1 0 0 1
0 0 1 0
0 0 0 1
   


     
   
     
   

     

   
     
   
     
   
     
   
   










Câu 2
Tịnh tiến ABCD sao cho điểm A tiến về gốc toạ độ O
1
1 0 0 6
0 1 0 5
()
0 0 1 0
0 0 0 1
M T A




  




Biến đổi kích thước hình chữ nhật từ 6x3 về hình chữ nhật kích thước 3x4
2
1

0 0 0
2
4
0 0 0
3
4
( , ,1)
3
63
0 0 1 0
0 0 0 1
MS









Thực hiện phép trượt đối với hình chữ nhật theo chiều Oy để nó trở thành hình bình hành
3
1 0 0 0
1
1 0 0
3
0 0 1 0
0 0 0 1
M Sh










Tịnh tiến hình bình hành sao cho đỉnh A từ O tiến về vị trí đỉnh A‘ như kết quả
4
1 0 0 0
0 1 0 1
(0, 1,0)
0 0 1 0
0 0 0 1
MT




  




Kết quả như sau:
4 3 2 1
* * *
1

0 0 0
1 0 0 0
1 0 0 0 1 0 0 6
2
1
1 0 0
4
0 1 0 1 0 1 0 5
0 0 0
3
* * *
3
0 0 1 0 0 0 1 0
0 0 1 0
0 0 1 0
0 0 0 1 0 0 0 1
0 0 0 1
0 0 0 1
1
0 0 3
2
20
14
0
6 3 3
0 0 1 0
0 0 0 1
M M M M



   


   



   



   


   


   












Câu 3
Chương trình hoàn chỉnh như sau
Sử dụng hàm OnDisplay_cau3a và OnDisplay_cau3b để hiển thị ra kết quả của câu 3a, 3b
#include <Windows.h>
#include <gl/GL.h>
#include <gl/glut.h>
#include <math.h>

#define SPACE 0.3
int moving, startx, starty;
GLfloat angle = 0; /* in degrees */
GLfloat angle2 = 0; /* in degrees */

void drawCube() {
glBegin(GL_TRIANGLE_STRIP);
glVertex3f(0.1f, 0.1f, 0.1f);
glVertex3f(0.1f, -0.1f, 0.1f);

glVertex3f(0.1f, 0.1f, -0.1f);
glVertex3f(0.1f, -0.1f, -0.1f);

glVertex3f(-0.1f, 0.1f, -0.1f);
glVertex3f(-0.1f, -0.1f, -0.1f);

glVertex3f(-0.1f, 0.1f, 0.1f);
glVertex3f(-0.1f, -0.1f, 0.1f);

glVertex3f(0.1f, 0.1f, 0.1f);
glVertex3f(0.1f, -0.1f, 0.1f);
glEnd();

glBegin(GL_TRIANGLE_STRIP);
glVertex3f(0.1f, 0.1f, 0.1f);
glVertex3f(0.1f, 0.1f, -0.1f);
glVertex3f(-0.1f, 0.1f, 0.1f);
glVertex3f(-0.1f, 0.1f, -0.1f);
glEnd();

glBegin(GL_TRIANGLE_STRIP);
glVertex3f(0.1f, -0.1f, 0.1f);
glVertex3f(0.1f, -0.1f, -0.1f);
glVertex3f(-0.1f, -0.1f, 0.1f);
glVertex3f(-0.1f, -0.1f, -0.1f);
glEnd();
}

void OnDisplay_cau3a(){
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LESS);
//glDisable(GL_COLOR_LOGIC_OP);
glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-4, 4, -4, 4, -100, 100);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(angle2, 1.0, 0.0, 0.0);
glRotatef(angle, 0.0, 1.0, 0.0);

float fScale;
for(int i = 0; i<9; i++)
{
glPushMatrix();
glColor3f(1.0f, 0.0f, 0.0f);
//Ve hinh lap phuong tren truc Ox
glTranslated(SPACE*i, 0, 0);
drawCube();

//Ve canh chu V trong mat phang xOy
fScale = 1;
glColor3f(0.0f, 1.0f, 0.0f);
for(int j = 0; j< 8 -i ; j++)
{
glPushMatrix();
glTranslated(0, SPACE*(j+1), 0);
drawCube();
glPopMatrix();
}

//Ve canh chu V trong mat phang xOz
fScale = 1;
glColor3f(0.0f, 0.0f, 1.0f);
for(int j = 0; j< 8 -i ; j++)
{
glPushMatrix();
glTranslated(0, 0, SPACE*(j+1));
drawCube();
glPopMatrix();
}

glPopMatrix();
}

glutSwapBuffers();
}

void OnDisplay_cau3b(){
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LESS);
//glDisable(GL_COLOR_LOGIC_OP);
glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-4, 4, -4, 4, -100, 100);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(angle2, 1.0, 0.0, 0.0);
glRotatef(angle, 0.0, 1.0, 0.0);

float fScale = 1.0f;
float fRotate = 0.0f;

glColor3f(0.0f, 0.0f, 0.0f);
drawCube();
for(int i = 1; i<10; i++)
{
fScale *= 0.9f;
fRotate += 22.5f;

glPushMatrix();

glColor3f(1.0f, 0.0f, 0.0f);
glPushMatrix();
glTranslatef(-SPACE*i, 0.0f, 0.0f);
glRotatef(fRotate, 1.0f, 0.0f, 0.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();
glPushMatrix();
glTranslatef(SPACE*i, 0.0f, 0.0f);
glRotatef(fRotate, 1.0f, 0.0f, 0.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();

glColor3f(0.0f, 1.0f, 0.0f);
glPushMatrix();
glTranslatef(0.0f, -SPACE*i, 0.0f);
glRotatef(fRotate, 0.0f, 1.0f, 0.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();
glPushMatrix();
glTranslatef(0.0f, SPACE*i, 0.0f);
glRotatef(fRotate, 0.0f, 1.0f, 0.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();

glColor3f(0.0f, 0.0f, 1.0f);
glPushMatrix();
glTranslatef(0.0f, 0.0f, -SPACE*i);
glRotatef(fRotate, 0.0f, 0.0f, 1.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();
glPushMatrix();
glTranslatef(0.0f, 0.0f, SPACE*i);
glRotatef(fRotate, 0.0f, 0.0f, 1.0f);
glScalef(fScale, fScale, fScale);
drawCube();
glPopMatrix();

glPopMatrix();
}

glutSwapBuffers();
}

void OnMouseMove(int x, int y)
{
if (moving) {
angle = angle + (x - startx)*0.1;
angle2 = angle2 + (y - starty)*0.1;
startx = x;
starty = y;
glutPostRedisplay();
}

}

void OnMouse(int button, int state, int x, int y) {
if (button == GLUT_LEFT_BUTTON) {
if (state == GLUT_DOWN) {
moving = 1;
startx = x;
starty = y;
}
if (state == GLUT_UP) {
moving = 0;
}
}
}

int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGBA | GLUT_DEPTH);
glutInitWindowSize(800, 800);
glutCreateWindow("simple");
glutDisplayFunc(OnDisplay_cau3b);
glutMouseFunc(OnMouse);
glutMotionFunc(OnMouseMove);

glutMainLoop();
}

Câu 4
5. glTranslatef(3f, 2f, 1f);

6. glRotatef(60f, 0f, 0f, 1f);
7. glScalef(2.5f, 1f, 1.5f);
8. glRotatef(90f, 0f, 0f, 1f);
R
z
(90
0
)S(2.5, 1, 1.5)R
z
(60
0
)T(3,2,1)
3
1
00
1 0 0 3 2.5 0 0 0 0 1 0 0
22
0 1 0 2 0 1 0 0 1 0 0 0
3
1
00
* * *
22
0 0 1 1 0 0 1.5 0 0 0 1 0
0 0 1 0
0 0 0 1 0 0 0 1 0 0 0 1
0 0 0 1
3
1.25 0 3
2

0.5 1.25 3 0 2
0 0 1.5 1
0 0 0 1



     

     

     

     

     

     













Câu 5
#include <Windows.h>
#include <gl/GL.h>
#include <gl/glut.h>
#include <math.h>

int iWnd;
float sqrt2 = sqrt(2.0);

struct SPOSITION {
float x, y;
SPOSITION(float x, float y):x(x), y(y) {}
};

struct SCOLOR {
float r, g, b;
SCOLOR(int r, int g, int b): r(r/255.0f), g(g/255.0f), b(b/255.0f) {}
};

void drawSquare(float r, float g, float b) {
glColor3f(r, g, b);
glBegin(GL_POLYGON);
glVertex2f( 5f, .5f);
glVertex2f( 5f, 5f);
glVertex2f(.5f, 5f);
glVertex2f(.5f, .5f);
glEnd();
}

void drawSquareAt(SPOSITION origin, SCOLOR color, float edge) {

glPushMatrix();
glTranslatef(origin.x, origin.y, 0);
glRotatef(45, 0, 0, 1);
glScalef(edge, edge, edge);
glPolygonMode(GL_FRONT, GL_FILL);
drawSquare(color.r, color.g, color.b);
glPolygonMode(GL_FRONT, GL_LINE);
drawSquare(0, 0, 0);
glPopMatrix();
}

#define ORANGE SCOLOR(230, 130, 0)
#define SKY SCOLOR(160, 215, 225)
#define VIOLET SCOLOR(190, 180, 210)
#define PINK SCOLOR(225, 170, 160)
#define YELLOW SCOLOR(255, 255, 0)
#define BROWN SCOLOR(170, 75, 65)

void drawTessellation(int row=6, int col=8) {
for (int x=0; x<col*2; x++)
for (int y=0; y<row*2; y++) {
if (x==0 || y==0) continue;
//ORANGE
if (x%4 == 2 && y %2 == 1)
drawSquareAt(SPOSITION(x, y), ORANGE, sqrt2);
//SKY
if (x%4 == 1 && y %4 == 2)
drawSquareAt(SPOSITION(x, y), SKY, sqrt2);
//VIOLET
if (x%4 == 3 && y %4 == 2)

drawSquareAt(SPOSITION(x, y), VIOLET, sqrt2);
//PINK
if (x%4 == 0 && y %2 == 1 && y!=1 && y!= row*2-1)
drawSquareAt(SPOSITION(x, y), PINK, sqrt2);
//YELLOW
if (x%4 == 3 && y %4 == 0 && x!= col*2-1)
drawSquareAt(SPOSITION(x, y), YELLOW, sqrt2);
//BROWN
if (x%4 == 1 && y %4 == 0 && x!=1)
drawSquareAt(SPOSITION(x, y), BROWN, sqrt2);
}
}

void drawGrid() {
for (int i=0; i< 50; i++) {
glBegin(GL_QUAD_STRIP);
for (int j=0; j< 50; j++) {
glVertex2i(i, j);
glVertex2i(i+1, j);
}
glEnd();
}
}

void OnDisplay(){
glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-5, 20, -5, 20, 0, 1);

glMatrixMode(GL_MODELVIEW);
glLoadIdentity();

drawTessellation();
//drawGrid();
glutSwapBuffers();
}

int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGBA);
glutInitWindowSize(400, 400);
iWnd = glutCreateWindow("simple");
glutDisplayFunc(OnDisplay);
glutMainLoop();
}