How to compute vertex normals for a triangle mesh in OpenGl? - c++

Question

To give background, I'm currently generating a surface of revolution with it's center of mass centered at (0,0,0) in the WCS. The surface of a revolution is y=x^2 where 0 <= x <= 1.
I have converted this surface of revolution into a virtual buffer object, and can render it successfully on the screen. However, I cannot seem to get Blinn-Phong shading to work on the object. I'm fairly sure that the problem lies in my normal calculation.
This is the stub that creates the object and calculates normals:
GLfloat vp[49 * 49 * 18]; // array of vertex points
int _i = 50;
int _j = 50;
float vertices[50][50][3];
for (int i = 0; i < _i; i++) {
float fT = (float) i / (_i - 1);
float fY = fT;
float fZ = sqrt(fT);
for (int j = 0; j < _j; j++) {
float fS = 2 * M_PI * (float) j / (_j - 1);
vertices[i][j][0] = fZ * cos(fS);
vertices[i][j][1] = fY - 0.5; // offset by 0.5 to make center of mass the center
vertices[i][j][2] = fZ * sin(fS);
}
}
int curr = 0;
for (int i = 0; i < _i - 1; i++) {
for (int j = 0; j < _j - 1; j++) {
vp[curr++] = vertices[i][j][0];
vp[curr++] = vertices[i][j][1];
vp[curr++] = vertices[i][j][2];
vp[curr++] = vertices[i+1][j][0];
vp[curr++] = vertices[i+1][j][1];
vp[curr++] = vertices[i+1][j][2];
vp[curr++] = vertices[i][j+1][0];
vp[curr++] = vertices[i][j+1][1];
vp[curr++] = vertices[i][j+1][2];
vp[curr++] = vertices[i+1][j][0];
vp[curr++] = vertices[i+1][j][1];
vp[curr++] = vertices[i+1][j][2];
vp[curr++] = vertices[i+1][j+1][0];
vp[curr++] = vertices[i+1][j+1][1];
vp[curr++] = vertices[i+1][j+1][2];
vp[curr++] = vertices[i][j+1][0];
vp[curr++] = vertices[i][j+1][1];
vp[curr++] = vertices[i][j+1][2];
}
}
GLuint vao;
glGenVertexArrays (1, &vao); // generating and binding is common pattern in OpenGL
glBindVertexArray (vao); // basically setting up memory and associating it
GLuint points_vbo;
glGenBuffers(1, &points_vbo);
glBindBuffer(GL_ARRAY_BUFFER, points_vbo);
glBufferData(GL_ARRAY_BUFFER, 49 * 49 * 18 * sizeof (GLfloat), vp, GL_STATIC_DRAW);
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, NULL);
glEnableVertexAttribArray(0);
GLfloat normals[49 * 49 * 18 / 3];
curr = 0;
for (int i = 0; i < 49 * 49 * 18; i += 9){
int Ux = vp[i+3] - vp[i];
int Uy = vp[i+4] - vp[i+1];
int Uz = vp[i+5] - vp[i+2];
int Vx = vp[i+6] - vp[i];
int Vy = vp[i+7] - vp[i+1];
int Vz = vp[i+8] - vp[i+2];
normals[curr++] = Uy * Vz - Uz * Vy;
normals[curr++] = Uz * Vx - Ux * Vz;
normals[curr++] = Ux * Vy - Uy * Vx;
}
GLuint normals_vbo;
glGenBuffers(1, &normals_vbo);
glBindBuffer(GL_ARRAY_BUFFER, normals_vbo);
glBufferData(GL_ARRAY_BUFFER, 49 * 49 * 18 / 3 * sizeof(GLfloat), normals, GL_STATIC_DRAW);
glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, 0, NULL);
glEnableVertexAttribArray(1);
This is my vertex shader:
#version 410
layout (location = 0) in vec3 vtxPosition;
layout (location = 1) in vec3 normal;
uniform mat4 proj_mat, view_mat, model_mat;
out vec3 Normal;
out vec3 fpos;
void main () {
gl_Position = proj_mat * view_mat * model_mat * vec4(vtxPosition, 1.0);
fpos = vec3(model_mat * vec4(vtxPosition, 1.0));
Normal = normal;
}
And lastly my fragment shader:
#version 410
// Define INPUTS from fragment shader
//uniform mat4 view_mat;
in vec3 Normal;
in vec3 fpos;
// These come from the VAO for texture coordinates.
in vec2 texture_coords;
// And from the uniform outputs for the textures setup in main.cpp.
uniform sampler2D texture00;
uniform sampler2D texture01;
out vec4 fragment_color; //RGBA color
const vec3 lightPos = vec3(0.0,0.0,5.0);
const vec3 diffColor = vec3(1.0,0.5,0.0);
const vec3 specColor = vec3(1.0,1.0,1.0);
void main () {
vec3 normal = normalize(Normal);
vec3 lightDir = normalize(lightPos - fpos);
float lamb = max(dot(lightDir, normal), 0.0);
float spec = 0.0;
if (lamb > 0.0) {
vec3 refDir = reflect(-lightDir, normal);
vec3 viewDir = normalize(-fpos);
float specAngle = max(dot(refDir, viewDir), 0.0);
spec = pow(specAngle, 4.0);
}
fragment_color = vec4(lamb * diffColor + spec * specColor, 1.0);
}
This is the current rendering of the object:

Answer 1

You have to specify 1 normal attribute for each vertex coordinate. A vertex coordinate and its attributes form a tuple.
Furthermore you have to use the data type float rather than int, for computing the normal vectors:
GLfloat normals[49 * 49 * 18];
curr = 0;
for (int i = 0; i < 49 * 49 * 18; i += 9){
float Ux = vp[i+3] - vp[i];
float Uy = vp[i+4] - vp[i+1];
float Uz = vp[i+5] - vp[i+2];
float Vx = vp[i+6] - vp[i];
float Vy = vp[i+7] - vp[i+1];
float Vz = vp[i+8] - vp[i+2];
float nx = Uy * Vz - Uz * Vy;
float ny = Uz * Vx - Ux * Vz;
float nz = Ux * Vy - Uy * Vx;
for (int j = 0; j < 3; ++j) {
normals[curr++] = nx;
normals[curr++] = ny;
normals[curr++] = nz;
}
}
glBufferData(GL_ARRAY_BUFFER, 49 * 49 * 18 * sizeof(GLfloat), normals, GL_STATIC_DRAW);
I recommend to invert the normal vector of the back faces for a double sided light model:
vec3 normal = normalize(Normal);
vec3 viewDir = normalize(-fpos);
if (dot(normal, viewDir) < 0.0)
normal *= -1.0;
Fragment shader:
#version 410
// Define INPUTS from fragment shader
//uniform mat4 view_mat;
in vec3 Normal;
in vec3 fpos;
// These come from the VAO for texture coordinates.
in vec2 texture_coords;
// And from the uniform outputs for the textures setup in main.cpp.
uniform sampler2D texture00;
uniform sampler2D texture01;
out vec4 fragment_color; //RGBA color
const vec3 lightPos = vec3(0.0,0.0,5.0);
const vec3 diffColor = vec3(1.0,0.5,0.0);
const vec3 specColor = vec3(1.0,1.0,1.0);
void main () {
vec3 normal = normalize(Normal);
vec3 viewDir = normalize(-fpos);
if (dot(normal, viewDir) < 0.0)
normal *= -1.0;
vec3 lightDir = normalize(lightPos - fpos);
float lamb = max(dot(lightDir, normal), 0.0);
float spec = 0.0;
if (lamb > 0.0) {
vec3 refDir = reflect(-lightDir, normal);
float specAngle = max(dot(refDir, viewDir), 0.0);
spec = pow(specAngle, 4.0);
}
fragment_color = vec4(lamb * diffColor + spec * specColor, 1.0);
}