OpenGL / GLUT是我的照明方法吗？
我被要求使用GL_TRIANGLE_STRIP制作一个简单的螺旋桨。但是，编写结构并不难，但是当我使用GL_TRIANGLE_STRIP时，让灯光正常工作会给我带来麻烦。在我使用GL_POLYGON并为形状（例如矩形）制作光照之前，我只需为每个形状指定glNormal3f一次。
问题：基于一些互联网搜索，显然我需要为每个形状指定涡旋的法线向量。那么我当前的灯光（我指定法线向量的方式）是否正确？
#include <GL/glut.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define PI 3.14159265
static GLfloat lpos[] = { 0.0, 0.0, 4.0, 1.0 };
static GLfloat white[] = { 1.0, 1.0, 1.0, 1.0 };
static GLfloat black[] = { 0.0, 0.0, 0.0, 1.0 };
static GLfloat red[] = { 1.0, 0.0, 0.0, 1.0 };
static GLfloat yellow[] = { 1.0, 1.0, 0.0, 1.0 };
static float alpha = 0.0;
static float beta = PI / 6.0;
static float zoom = 10.0;
static bool lightSource = true;
float twistConstant = 0;
float rotateConstant = 0;
float numberOfObj = 3;
float numberOfTriangles = 1;
static GLdouble cpos[3];
void DrawTopTriangleSet(){
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, yellow);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, yellow);
glBegin(GL_TRIANGLE_STRIP);
for (int i = 180; i >= 0; i = i - numberOfTriangles){
glNormal3f(0, cos(i*PI / 180), sin(i*PI / 180));
glVertex3f(i*PI / 180, 0, 0.5*sin(i*PI / 180));
glVertex3f(i*PI / 180, 0.5*sin(i*PI / 180), twistConstant*-sin(i*PI / 180));
}
glEnd();
}
void DrawBottomTriangleSet(){
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, yellow);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, yellow);
glBegin(GL_TRIANGLE_STRIP);
for (int i = 180; i >= 0; i = i - numberOfTriangles){
glNormal3f(0, -cos(i*PI / 180), sin(i*PI / 180));
glVertex3f(i*PI / 180, -0.5*sin(i*PI / 180), twistConstant*sin(i*PI / 180));
glVertex3f(i*PI / 180, 0, 0.5*sin(i*PI / 180));
}
glEnd();
}
void DrawBackTriangleSet(){
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, yellow);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, yellow);
glBegin(GL_TRIANGLE_STRIP);
for (int i = 180; i >= 0; i = i - numberOfTriangles){
glNormal3f(0, -cos(i*PI / 180), -sin(i*PI / 180));
glVertex3f(i*PI / 180, 0.5*sin(i*PI / 180), twistConstant*-sin(i*PI / 180));
glVertex3f(i*PI / 180, -0.5*sin(i*PI / 180), twistConstant*sin(i*PI / 180));
}
glEnd();
}
void DrawInsideTriangleSet(){
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glBegin(GL_TRIANGLE_STRIP);
for (int i = 180; i >= 0; i = i - numberOfTriangles){
glVertex3f(i*PI / 180, 0.5*sin(i*PI / 180), twistConstant*-sin(i*PI / 180));
glVertex3f(i*PI / 180, 0, 0.5*sin(i*PI / 180));
glVertex3f(i*PI / 180, -0.5*sin(i*PI / 180), twistConstant*sin(i*PI / 180));
}
glEnd();
}
void writemessage()
{
printf(" X => x++ <= Move light source in direction of +X\n");
printf(" Y => y++ <= Move light source in direction of +Y\n");
printf(" Z => z++ <= Move light source in direction of +Z\n");
printf("\n");
printf("^X => x-- <= Move light source in direction of -X\n");
printf("^Y => y-- <= Move light source in direction of -Y\n");
printf("^Z => z-- <= Move light source in direction of -Z\n");
printf("\n");
printf(" ^ => Move camera up\n");
printf(" > => Move camera right\n");
printf(" < => Move camera left\n");
printf(" down arrow => Move camera down\n");
printf("\n");
printf(" t => More Twist\n");
printf(" f => Less Twist\n");
printf("\n");
printf(" q => More Propeller\n");
printf(" f => Less Propeller\n");
printf("\n");
printf(" w => More Triangles\n");
printf(" s => Less Triangles\n");
printf("\n");
printf(" 0 => Toggling light source\n");
printf("\n");
printf(" r => Rotates Propeller\n");
printf("\n");
printf(" You can not move the light source when the light source is off !!!");
}
void reshape(int w, int h)
{
glViewport(0, 0, (GLsizei)w, (GLsizei)h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(45.0, (GLfloat)w / (GLfloat)h, 0.01, 20.0);
glMatrixMode(GL_MODELVIEW);
}
void display(void)
{
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
cpos[0] = zoom * cos(beta) * sin(alpha);
cpos[1] = zoom * sin(beta);
cpos[2] = zoom * cos(beta) * cos(alpha);
gluLookAt(cpos[0], cpos[1], cpos[2], 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
if (lightSource == true){
glLightfv(GL_LIGHT0, GL_POSITION, lpos);
glMaterialfv(GL_FRONT, GL_EMISSION, white);
glPushMatrix();
glTranslatef(lpos[0], lpos[1], lpos[2]);
glutSolidSphere(0.1, 10, 8);
glPopMatrix();
glMaterialfv(GL_FRONT, GL_EMISSION, black);
}
glRotatef(rotateConstant, 0, 0, 1);
for (int i = 0; i < numberOfObj; i++){
glPushMatrix();
glRotatef(i * 360 / numberOfObj, 0, 0, 1);
DrawTopTriangleSet();
DrawBottomTriangleSet();
DrawBackTriangleSet();
DrawInsideTriangleSet();
glPopMatrix();
}
// Cone
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, red);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, red);
glPushMatrix();
glTranslated(0, 0, -1.5);
glutSolidCone(1, 2, 50, 50);
glPopMatrix();
// Back of Cone
glMaterialfv(GL_FRONT, GL_EMISSION, black);
glMaterialfv(GL_BACK, GL_EMISSION, black);
glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, red);
glMaterialfv(GL_BACK, GL_AMBIENT_AND_DIFFUSE, red);
glBegin(GL_POLYGON);
glNormal3f(0, 0, 1);
for (int i = 0; i <= 360; i++)
{
glVertex3f(cos(i*PI / 180) * 1, sin(i*PI / 180) * 1, -1.5);
}
glEnd();
glutSwapBuffers();
glFlush();
}
void keyboard(unsigned char key, int x, int y)
{
switch (key) {
case 27:
exit(0);
break;
case 'x':
if (lightSource == true)
lpos[0] = lpos[0] + 0.2;
glutPostRedisplay();
break;
case 'X':
if (lightSource == true)
lpos[0] = lpos[0] - 0.2;
glutPostRedisplay();
break;
case 'y':
if (lightSource == true)
lpos[1] = lpos[1] + 0.2;
glutPostRedisplay();
break;
case 'Y':
if (lightSource == true)
lpos[1] = lpos[1] - 0.2;
glutPostRedisplay();
break;
case 'z':
if (lightSource == true)
lpos[2] = lpos[2] + 0.2;
glutPostRedisplay();
break;
case 'Z':
if (lightSource == true)
lpos[2] = lpos[2] - 0.2;
glutPostRedisplay();
break;
case '+':
if (zoom != 1.5)zoom = zoom - 0.5;
glutPostRedisplay();
break;
case '-':
if (zoom != 15)zoom = zoom + 0.5;
glutPostRedisplay();
break;
case '0':
if (lightSource == true){
glDisable(GL_LIGHT0);
lightSource = false;
}
else{
glEnable(GL_LIGHT0);
lightSource = true;
}
glutPostRedisplay();
break;
case 't':
if (twistConstant <= 1){
twistConstant = twistConstant + 0.05;
glutPostRedisplay();
}
break;
case 'f':
if (twistConstant >= 0){
twistConstant = twistConstant - 0.05;
glutPostRedisplay();
}
break;
case 'r':
rotateConstant = rotateConstant + 2;
glutPostRedisplay();
break;
case 'q':
if (numberOfObj <= 6){
numberOfObj++;
glutPostRedisplay();
}
break;
case 'a':
if (numberOfObj >= 0){
numberOfObj--;
glutPostRedisplay();
}
break;
case 's':
if (numberOfTriangles <90){
numberOfTriangles++;
glutPostRedisplay();
}
break;
case 'w':
if (numberOfTriangles > 1){
numberOfTriangles--;
glutPostRedisplay();
}
break;
default:
break;
}
}
void specialkey(GLint key, int x, int y)
{
switch (key) {
case GLUT_KEY_RIGHT:
alpha = alpha + PI / 180;
if (alpha > 2 * PI) alpha = alpha - 2 * PI;
glutPostRedisplay();
break;
case GLUT_KEY_LEFT:
alpha = alpha - PI / 180;
if (alpha < 0) alpha = alpha + 2 * PI;
glutPostRedisplay();
break;
case GLUT_KEY_UP:
if (beta < 0.45*PI) beta = beta + PI / 180;
glutPostRedisplay();
break;
case GLUT_KEY_DOWN:
if (beta > -0.05*PI) beta = beta - PI / 180;
glutPostRedisplay();
break;
default:
break;
}
}
int main(int argc, char** argv)
{
writemessage();
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
glutInitWindowSize(1200, 800);
glutInitWindowPosition(0, 0);
glutCreateWindow(argv[0]);
glClearColor(0.0, 0.0, 0.0, 0.0);
glEnable(GL_DEPTH_TEST);
glShadeModel(GL_SMOOTH);
glEnable(GL_LIGHTING);
glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
glEnable(GL_LIGHT0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
gluLookAt(0.0, 5.0, 10.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0);
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutKeyboardFunc(keyboard);
glutSpecialFunc(specialkey);
glutMainLoop();
return 0;
}
1 个答案:
答案 0 :(得分：4)
我不认为你的法线是正确的。例如，对于几何体的这一部分：
glNormal3f(0, cos(i*PI / 180), sin(i*PI / 180));
glVertex3f(i*PI / 180, 0, 0.5*sin(i*PI / 180));
glVertex3f(i*PI / 180, 0.5*sin(i*PI / 180), twistConstant*-sin(i*PI / 180));
由于twistConstant是顶点坐标计算的一部分，因此它看起来非常可疑，它也不是正常计算的一部分。如果法线改变顶点的计算方式，我认为法线不可能不依赖于常数值。
让我们试着计算一下这种情况的正常情况。这只是为了说明这个过程，如果不尝试，我很可能不会完全正确。
对于参数化曲面，通常将法线计算为两个梯度向量的交叉乘积（每个参数对应一个）。使用a缩写为I * PI / 180的角度，c为twistConstant的缩写，上述代码中的两个顶点为：
| a | | a |
v1 = | 0 | v2 = | 0.5 * sin(a) |
| 0.5 * sin(a) | | - c * sin(a) |
顶点a处参数v1的渐变是：
| 1 |
dv1 / da = | 0 |
| 0.5 * cos(a) |
我读代码的方式，表面在这两个顶点之间的方向是平的，所以我们可以使用两个向量之间的差异作为第二个渐变：
| 0 |
v2 - v1 = | 0.5 * sin(a) |
| - (c + 0.5) * sin(a) |
这两个梯度向量之间的叉积是：
| 1 | | 0 | | -0.25 * sin(a) * cos(a) |
| 0 | x | 0.5 * sin(a) | = | (c + 0.5) * sin(a) |
| 0.5 * cos(a) | | - (c + 0.5) * sin(a) | | 0.5 * sin(a) |
这将是顶点v1处的法线。 v2处的法线将是不同的，这是有道理的，因为刀片是扭曲的。
除了数学之外，您还缺少在DrawInsideTriangleSet()中指定法线：
glVertex3f(i*PI / 180, 0.5*sin(i*PI / 180), twistConstant*-sin(i*PI / 180));
glVertex3f(i*PI / 180, 0, 0.5*sin(i*PI / 180));
glVertex3f(i*PI / 180, -0.5*sin(i*PI / 180), twistConstant*sin(i*PI / 180));
第一个电话可能应该是glNormal3f()而不是glVertex3f()。
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