OpenGL: How do I render individual RGB values given a cross product that contains the total light?
I've been working on my own implementation of a Gouraud style shading model, and I've got the rest of it working pretty much how I want it, but the problem I've run into is it only shows white light. The calc_color function is where this operation is being performed. The Color variable represents the total light of the R, G and B values for that given location. I've been assigning Color to all three arrays just to get the shading implemented properly, but now that that is complete, I'd like to figure out a way to extract the R, G and B values from that total light value.
I've tried several different things, like taking the total light, and taking a percentage of the Light1r, etc. values but it always ends up looking strange or too bright.
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#ifdef MAC
#include <GLUT/glut.h>
#else
#include <GL/glut.h>
#endif
using namespace std;
//Camera variables
int xangle = -270;
int yangle = 0;
//Control Modes (Rotate mode by default)
int mode = 0;
int lightmode = 0;
//Player Position (Y offset so it would not be straddling the grid)
float cubeX = 0;
float cubeY = 0.5;
float cubeZ = 0;
//Vertex arrays for surface
float surfaceX [12][12];
float surfaceY [12][12];
float surfaceZ [12][12];
//Surface Normal arrays
float Nx[11][11];
float Ny[11][11];
float Nz[11][11];
//Color arrays
float R[11][11];
float G[11][11];
float B[11][11];
//Light position and color variables
float Light1x = 0;
float Light1y = 5;
float Light1z = 0;
float Light1r = 0;
float Light1g = 1;
float Light1b = 0;
float Light2x = -5;
float Light2y = 5;
float Light2z = -5;
float Light2r = 0;
float Light2g = 1;
float Light2b = 0;
//Random number generator
float RandomNumber(float Min, float Max)
{
return ((float(rand()) / float(RAND_MAX)) * (Max - Min)) + Min;
}
//---------------------------------------
// Initialize surface
//---------------------------------------
void init_surface()
{
//Initialize X, select column
for (int i = 0; i < 12; i++)
{
//Select row
//Surface is +1 so the far right normal will be generated correctly
for (int j = 0; j < 12; j++)
{
//-5 to compensate for negative coordinate values
surfaceX[i][j] = i-5;
//Generate random surface height
surfaceY[i][j] = RandomNumber(5, 7) - 5;
//surfaceY[i][j] = 0;
surfaceZ[i][j] = j-5;
}
}
}
void define_normals()
{
//Define surface normals
for (int i = 0; i < 11; i++)
{
for (int j = 0; j < 11; j++)
{
//Get two tangent vectors
float Ix = surfaceX[i+1][j] - surfaceX[i][j];
float Iy = surfaceY[i+1][j] - surfaceY[i][j];
float Iz = surfaceZ[i+1][j] - surfaceZ[i][j];
float Jx = surfaceX[i][j+1] - surfaceX[i][j];
float Jy = surfaceY[i][j+1] - surfaceY[i][j];
float Jz = surfaceZ[i][j+1] - surfaceZ[i][j];
//Do cross product, inverted for upward normals
Nx[i][j] = - Iy * Jz + Iz * Jy;
Ny[i][j] = - Iz * Jx + Ix * Jz;
Nz[i][j] = - Ix * Jy + Iy * Jx;
//Original vectors
//Nx[i][j] = Iy * Jz - Iz * Jy;
//Ny[i][j] = Iz * Jx - Ix * Jz;
//Nz[i][j] = Ix * Jy - Iy * Jx;
float length = sqrt(
Nx[i][j] * Nx[i][j] +
Ny[i][j] * Ny[i][j] +
Nz[i][j] * Nz[i][j]);
if (length > 0)
{
Nx[i][j] /= length;
Ny[j][j] /= length;
Nz[i][j] /= length;
}
}
}
}
void calc_color()
{
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
//Calculate light vector
//Light position, hardcoded for now 0,1,1
float Lx = Light1x - surfaceX[i][j];
float Ly = Light1y - surfaceY[i][j];
float Lz = Light1z - surfaceZ[i][j];
float length = sqrt(Lx * Lx + Ly * Ly + Lz * Lz);
if (length > 0)
{
Lx /= length;
Ly /= length;
Lz /= length;
}
//std::cout << "Lx: " << Lx << std::endl;
//std::cout << "Ly: " << Ly << std::endl;
//std::cout << "Lz: " << Lz << std::endl;
//Grab surface normals
//These are Nx,Ny,Nz due to compiler issues
float Na = Nx[i][j];
float Nb = Ny[i][j];
float Nc = Nz[i][j];
//std::cout << "Na: " << Na << std::endl;
//std::cout << "Nb: " << Nb << std::endl;
//std::cout << "Nc: " << Nc << std::endl;
//Do cross product
float Color = (Na * Lx) + (Nb * Ly) + (Nc * Lz);
std::cout << "Color: " << Color << std::endl;
//if (Color > 0)
//{
// Color = Color / 100;
//}
//Percent of light color
//float Ramt = (Light1r/2) / Color;
//float Gamt = (Light1g/2) / Color;
//float Bamt = (Light1b/2) / Color;
//R[i][j] = Ramt * Color;
//G[i][j] = Gamt * Color;
//B[i][j] = Bamt * Color;
R[i][j] = Color;
G[i][j] = Color;
B[i][j] = Color;
}
}
}
//---------------------------------------
// Init function for OpenGL
//---------------------------------------
void init()
{
glClearColor(0.0, 0.0, 0.0, 1.0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
//Viewing Window Modified
glOrtho(-7.0, 7.0, -7.0, 7.0, -7.0, 7.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
//Rotates camera
//glRotatef(30.0, 1.0, 1.0, 1.0);
glEnable(GL_DEPTH_TEST);
//Project 3 code
init_surface();
define_normals();
//Shading code
// glShadeModel(GL_SMOOTH);
// glEnable(GL_NORMALIZE);
//X,Y,Z - R,G,B
// init_light(GL_LIGHT1, Light1x, Light1y, Light1z, Light1r, Light1g, Light1b);
// init_light(GL_LIGHT2, Light2x, Light2y, Light2z, Light2r, Light2g, Light2b);
//init_light(GL_LIGHT2, 0, 1, 0, 0.5, 0.5, 0.5);
}
void keyboard(unsigned char key, int x, int y)
{
///TODO: allow user to change color of light
//Controls
//Toggle Mode
if (key == 'q')
{
if(mode == 0)
{
mode = 1;
std::cout << "Switched to Light mode (" << mode << ")" << std::endl;
}
else if(mode == 1)
{
mode = 0;
std::cout << "Switched to Rotate mode (" << mode << ")" << std::endl;
}
}
//Toggle light control
else if (key == 'e' && mode == 1)
{
if(lightmode == 0)
{
lightmode = 1;
std::cout << "Switched to controlling light 2 (" << lightmode << ")" << std::endl;
}
else if(lightmode == 1)
{
lightmode = 0;
std::cout << "Switched to controlling light 1 (" << lightmode << ")" << std::endl;
}
}
////Rotate Camera (mode 0)
//Up & Down
else if (key == 's' && mode == 0)
xangle += 5;
else if (key == 'w' && mode == 0)
xangle -= 5;
//Left & Right
else if (key == 'a' && mode == 0)
yangle -= 5;
else if (key == 'd' && mode == 0)
yangle += 5;
////Move Light (mode 1)
//Forward & Back
else if (key == 'w' && mode == 1)
{
if (lightmode == 0)
{
Light1z = Light1z - 1;
//init_surface();
//define_normals();
//calc_color();
//glutPostRedisplay();
}
else if (lightmode == 1)
Light2z = Light2z - 1;
//init_surface();
}
else if (key == 's' && mode == 1)
{
if (lightmode == 0)
Light1z = Light1z + 1;
else if (lightmode == 1)
Light2z = Light2z + 1;
}
//Strafe
else if (key == 'd' && mode == 1)
{
if (lightmode == 0)
Light1x = Light1x + 1;
else if (lightmode == 1)
Light2x = Light2x + 1;
}
else if (key == 'a' && mode == 1)
{
if (lightmode == 0)
Light1x = Light1x - 1;
else if (lightmode == 1)
Light2x = Light2x - 1;
}
//Up & Down (Cube offset by +0.5 in Y)
else if (key == 'z' && mode == 1)
{
if (lightmode == 0)
Light1y = Light1y + 1;
else if (lightmode == 1)
Light2y = Light2y + 1;
}
else if (key == 'x' && mode == 1)
{
if (lightmode == 0)
Light1y = Light1y - 1;
else if (lightmode == 1)
Light2y = Light2y - 1;
}
//Redraw objects
glutPostRedisplay();
}
//---------------------------------------
// Display callback for OpenGL
//---------------------------------------
void display()
{
// Clear the screen
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
//Rotation Code
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(xangle, 1.0, 0.0, 0.0);
glRotatef(yangle, 0.0, 1.0, 0.0);
//Light Code
// init_material(Ka, Kd, Ks, 100 * Kp, 0.8, 0.6, 0.4);
// init_light(GL_LIGHT1, Light1x, Light1y, Light1z, Light1r, Light1g, Light1b);
// init_light(GL_LIGHT2, Light2x, Light2y, Light2z, Light2r, Light2g, Light2b);
// glEnable(GL_LIGHTING);
//Color Code
calc_color();
//Draw the squares, select column
for (int i = 0; i <= 9; i++)
{
//Select row
for (int j = 0; j <= 9; j++)
{
glBegin(GL_POLYGON);
//Surface starts at top left
//Counter clockwise
glColor3f(R[i][j], G[i][j], B[i][j]);
std::cout << R[i][j] << " " << G[i][j] << " " << B[i][j] << endl;
// glNormal3f(Nx[i][j], Ny[i][j], Nz[i][j]);
glVertex3f(surfaceX[i][j], surfaceY[i][j], surfaceZ[i][j]);
glColor3f(R[i][j+1], G[i][j+1], B[i][j+1]);
// glNormal3f(Nx[i][j+1], Ny[i][j+1], Nz[i][j+1]);
glVertex3f(surfaceX[i][j+1], surfaceY[i][j+1], surfaceZ[i][j+1]);
glColor3f(R[i+1][j+1], G[i+1][j+1], B[i+1][j+1]);
// glNormal3f(Nx[i+1][j+1], Ny[i+1][j+1], Nz[i+1][j+1]);
glVertex3f(surfaceX[i+1][j+1], surfaceY[i+1][j+1], surfaceZ[i+1][j+1]);
glColor3f(R[i+1][j], G[i+1][j], B[i+1][j]);
// glNormal3f(Nx[i+1][j], Ny[i+1][j], Nz[i+1][j]);
glVertex3f(surfaceX[i+1][j], surfaceY[i+1][j], surfaceZ[i+1][j]);
glEnd();
}
}
// glDisable(GL_LIGHTING);
//Draw the normals
for (int i = 0; i <= 10; i++)
{
for (int j = 0; j <= 10; j++)
{
glBegin(GL_LINES);
glColor3f(0.0, 1.0, 1.0);
float length = 1;
glVertex3f(surfaceX[i][j], surfaceY[i][j], surfaceZ[i][j]);
glVertex3f(surfaceX[i][j]+length*Nx[i][j],
surfaceY[i][j]+length*Ny[i][j],
surfaceZ[i][j]+length*Nz[i][j]);
glEnd();
}
}
//Marking location of lights
glPointSize(10);
glBegin(GL_POINTS);
glColor3f(Light1r, Light1g, Light1b);
glVertex3f(Light1x, Light1y, Light1z);
glEnd();
glPointSize(10);
glBegin(GL_POINTS);
glColor3f(Light2r, Light2g, Light2b);
glVertex3f(Light2x, Light2y, Light2z);
glEnd();
//+Z = Moving TOWARD camera in opengl
//Origin point for reference
glPointSize(10);
glColor3f(1.0, 1.0, 0.0);
glBegin(GL_POINTS);
glVertex3f(0, 0, 0);
glEnd();
//Assign Color of Lines
float R = 1;
float G = 1;
float B = 1;
glBegin(GL_LINES);
glColor3f(R, G, B);
////Drawing the grid
//Vertical lines
for (int i = 0; i < 11; i++)
{
int b = -5 + i;
glVertex3f(b, 0, -5);
glVertex3f(b, 0, 5);
}
//Horizontal lines
for (int i = 0; i < 11; i++)
{
int b = -5 + i;
glVertex3f(-5,0,b);
glVertex3f(5,0,b);
}
glEnd();
glFlush();
}
//---------------------------------------
// Main program
//---------------------------------------
int main(int argc, char *argv[])
{
srand(time(NULL));
//Print Instructions
std::cout << "Project 3 Controls: " << std::endl;
std::cout << "q switches control mode" << std::endl;
std::cout << "w,a,s,d for camera rotation" << std::endl;
//Required
glutInit(&argc, argv);
//Window will default to a different size without
glutInitWindowSize(500, 500);
//Window will default to a different position without
glutInitWindowPosition(250, 250);
//
glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE | GLUT_DEPTH);
//Required
glutCreateWindow("Project 3");
//Required, calls display function
glutDisplayFunc(display);
glutKeyboardFunc(keyboard);
//Required
init();
glutMainLoop();
return 0;
}
Solution
A common formula to calculate a a diffuse light is to calculate the Dot product of the normal vector of the surface and the vector to from the surface to the light source. See How does this faking the light work on aerotwist?.
kd = max(0, L dot N)
To get the color of the light, the RGB values are component wise multiplied by the diffuse coefficient:
(Cr, Cg, Cb) = (LCr, LCg, LCb) * kd
If there are multiple light sources, then the light colors are summed:
(Cr, Cg, Cb) = (LC1r, LC1g, LC1b) * max(0, L1 dot N) + (LC2r, LC2g, LC2b) * max(0, L2 dot N)
Note, if the surface (material) has an additional color, then ths color would have to be component wise multiplied to the final color:
(Cr, Cg, Cb) = (Cr, Cg, Cb) * (CMr, CMg, CMb)
Write a function which calculates the light for 1 single light source and add the light to the final color:
void add_light_color(int i, int j, float lpx, float lpy, float lpz, float lcr, float lcg, float lcb)
{
float Lx = lpx - surfaceX[i][j];
float Ly = lpy - surfaceY[i][j];
float Lz = lpz - surfaceZ[i][j];
float length = sqrt(Lx * Lx + Ly * Ly + Lz * Lz);
if (length <= 0.0)
return;
float kd = Lx/length * Nx[i][j] + Ly/length * Ny[i][j] + Ly/length * Ny[i][j];
if ( kd <= 0.0 )
return;
R[i][j] += kd * lcr;
G[i][j] += kd * lcg;
B[i][j] += kd * lcb;
}
Traverse the filed of attributes, set each color (0, 0, 0) and use the above function to add the color form each light source:
void calc_color()
{
float lp1[] = {Light1x, Light1y, Light1z};
float lp2[] = {Light2x, Light2y, Light2z};
float lc1[] = {Light1r, Light1g, Light1b};
float lc2[] = {Light2r, Light2g, Light2b};
for (int i = 0; i < 10; i++)
{
for (int j = 0; j < 10; j++)
{
R[i][j] = G[i][j] = B[i][j] = 0.0;
add_light_color(i, j, Light1x, Light1y, Light1z, Light1r, Light1g, Light1b);
add_light_color(i, j, Light2x, Light2y, Light2z, Light2r, Light2g, Light2b);
}
}
}
The result for the following light color settings:
float Light1r = 1;
float Light1g = 0;
float Light1b = 0;
float Light2r = 0;
float Light2g = 1;
float Light2b = 0;
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