Cell-Shading Outlines: edge mesh writer does not define all desired edges - c++

Question

The program that I am writing takes in the vertex data of a 3D mesh, performs a series of calculations (forgive the vagueness, I'll try to explain in better detail later), and outputs a binary file that defines where the edges are on the mesh. My program then draws a colored line where the edge is. Without the appropriate vertex shader, this would look like a regular triangulated mesh, but once the appropriate vertex shader is applied, only the edges that are "sharp" (the dot product of their normals is greater than something close to zero) have lines drawn on them, along with the edges on the outside of the figure. My implementation for the outline is not correct, as I made the assumption that if an edge wasn't behind the edge, and didn't define a sharp edge, it would be an outline edge. I haven't found a satisfactory answer to this elsewhere, and I didn't want to rely on the old trick of re-drawing the mesh as a solid color, and rendering it to be slightly larger than the original mesh. This approach was to be entirely math-based, relying only on the vertex data of a mesh. I am writing a program that uses the following vertex shader:
uniform mat4 worldMatrix;
uniform mat4 projMatrix;
uniform mat4 viewProjMatrix;
uniform vec4 eyepos;
attribute vec3 a;
attribute vec3 b;
attribute vec3 n1;
attribute vec3 n2;
attribute float w;
void main()
{
float a_vertex = dot(eyepos.xyz - a, n1);
float b_vertex = dot(eyepos.xyz - a, n2);
if (a_vertex * b_vertex > 0.0) // signs are different, edge is behind the object
{
gl_Position = vec4(2.0,2.0,2.0,1.0);
}
else // the outline of the figure
{
if(w == 0.0)
{
vec4 p = vec4(a.x, a.y, a.z, 1.0);
p = p * worldMatrix * viewProjMatrix;
gl_Position = p;
}
else
{
vec4 p = vec4(b.x, b.y, b.z, 1.0);
p = p * worldMatrix * viewProjMatrix;
gl_Position = p;
}
}
if(dot(n1, n2) <= 0.2) // there is a sharp edge
{
if(w == 0.0)
{
vec4 p = vec4(a.x, a.y, a.z, 1.0);
p = p * worldMatrix * viewProjMatrix;
gl_Position = p;
}
else
{
vec4 p = vec4(b.x, b.y, b.z, 1.0);
p = p * worldMatrix * viewProjMatrix;
gl_Position = p;
}
}
}
... to take information from a binary file that is written using this program in C++:
#include <iostream>
#include "llgl.h"
#include <fstream>
#include <vector>
#include "SuperMesh.h"
using namespace std;
using namespace llgl;
struct Vertex
{
float x,y,z,w;
float s,t,p,q;
float nx,ny,nz,nw;
};
bool isFileAlright(string fName)
{
ifstream in(fName.c_str());
if(!in.good())
return false;
return true;
}
int main(int argc, char* argv[])
{
// INPUT FILE NAME //
string fName;
cout << "Enter the path to your spec.mesh file here: ";
cin >> fName;
while(!isFileAlright(fName))
{
cout << "Enter the path to your spec.mesh file here: ";
cin >> fName;
}
SuperMesh* Model = new SuperMesh(fName.c_str());
// END INPUT //
Model->load();
Model->draw();
string fname = Model->fname;
string FileName = fname.substr(0, fname.size() - 10); // supposed to slash the last 10 characters off of the string, removing ".spec.mesh"...
FileName = FileName + ".bin"; //... and then we make it a .bin file*/
cout << FileName << endl;
ofstream out(FileName.c_str(), ios::binary);
for (unsigned w = 0; w < Model->m.size(); w++)
{
vector<float> &vdata = Model->m[w]->vdata;
vector<char> &idata = Model->m[w]->idata;
//Create a vertex and index variable, a map for Edge Mesh, perform two loops to analyze all triangles on a mesh and write out their vertex values to a file.//
Vertex* V = (Vertex*)(&vdata[0]);
unsigned short* I16 = (unsigned short*)(&idata[0]);
unsigned char* I8 = (unsigned char*)(&idata[0]);
unsigned int* I32 = (unsigned int*)(&idata[0]);
map<set<int>, vector<vec3> > EM;
for(unsigned i = 0; i < Model->m[w]->ic; i += 3) // 3 because we're looking at triangles //
{
Mesh* foo = Model->m[w];
int i1;
int i2;
int i3;
if( Model->m[w]->ise == GL_UNSIGNED_BYTE)
{
i1 = I8[i];
i2 = I8[i + 1];
i3 = I8[i + 2];
}
else if( Model->m[w]->ise == GL_UNSIGNED_SHORT)
{
i1 = I16[i];
i2 = I16[i + 1];
i3 = I16[i + 2];
}
else
{
i1 = I32[i];
i2 = I32[i + 1];
i3 = I32[i + 2];
}
vec3 p = vec3(V[i1].x, V[i1].y, V[i1].z); // to represent the point in 3D space of each vertex on every triangle on the mesh
vec3 q = vec3(V[i2].x, V[i2].y, V[i2].z);
vec3 r = vec3(V[i3].x, V[i3].y, V[i3].z);
vec3 v1 = p - q;
vec3 v2 = r - q;
vec3 n = cross(v2,v1); //important to make sure the order is correct here, do VERTEX TWO dot VERTEX ONE//
set<int> tmp;
tmp.insert(i1); tmp.insert(i2);
EM[tmp].push_back(n);
set<int> tmp2;
tmp2.insert(i2); tmp2.insert(i3);
EM[tmp2].push_back(n);
set<int> tmp3;
tmp3.insert(i3); tmp3.insert(i1);
EM[tmp3].push_back(n);
//we have now pushed every needed point into our edge map
}
int edgeNumber = 0;
cout << "There should be 12 edges on a lousy cube." << endl;
for(map<set<int>, vector<vec3> >::iterator it = EM.begin(); it != EM.end(); ++it)
{
//Now we will take our edge map and write its data to the file!//
/* Information is written to the file in this form:
Vertex One, Vertex Two, Normal One, Normal Two, r (where r, depending on its value, determines whether one edge is on top of the other in the case
where two edges are aligned with one another)
*/
set<int>::iterator tmp = it->first.begin();
int pi = *tmp;
tmp++;
int qi = *tmp;
Vertex One = V[pi];
Vertex Two = V[qi];
vec3 norm1 = it->second[0];
vec3 norm2;
if(it->second.size() == 1)
norm2 = -1 * norm1;
else
norm2 = it->second[1];
out.write((char*) &One, 12);
out.write((char*) &Two, 12);
out.write((char*) &norm1, 12);
out.write((char*) &norm2, 12);
float r = 0;
out.write((char*) &r, 4);
out.write((char*) &One, 12);
out.write((char*) &Two, 12);
out.write((char*) &norm1, 12);
out.write((char*) &norm2, 12);
r = 1;
out.write((char*) &r, 4);
edgeNumber++;
cout << "Wrote edge #" << edgeNumber << endl;
}
}
return 0;
}
The problem that this program has is that it does neither of these two essential things in the test case where I use it to draw a simple box with outlines:
It does not draw outlines. The vertex shader is not sufficient to determine anything more than where the edges of the object are. The binary file that makes this happen is pre-computed in a separate program using code from the second snippet posted above, and then it is saved as a .bin file along with the mesh assets to which it belongs. However, raw vertex data would only take me so far, and I seek a way to draw a line around the outside of the mesh without using more traditional methods.
It does not draw ALL of the edges that I need. In my test case, two of the edges are missing, and I cannot figure out for the life of me why. I figure I must have done something wrong in writing the edge map.
A couple notes about the above code:
llgl is an OpenGL wrapper that I have used to simplify many elements of OpenGL. It is not used extensively here, but rather in the creation of meshes, done elsewhere.
Things like Mesh and SuperMesh (a collection of meshes into one rigid body) are meant to be 3D objects in my scene. In my test case, there is only one Mesh in my scene, and defining a SuperMesh of a single Mesh is essentially just creating a single Mesh.
The "draw" call in the second snippet, which pre-computes a Mesh's edge map, does not actually draw anything. It is necessary to gain access to the Mesh's vertex data.
The variable "ise" is taken from the individual Meshes in the SuperMesh, and is a variable found by reading it in from the original Blender .OBJ file. It is related to how much memory should be used to store the important vertex data. It generally isn't a good idea to allocate more space than is needed for these values, as I've been told by friends and mentors who work with Blender.
It isn't well-commented, as I'm not the only one who has worked on this code, and I, unfortunately, have a limited understanding of how the second snippet could iterate through all of the triangles on a mesh and somehow miss the last two edges. Once I understand better what this code should do when properly written, I plan on heavily commenting it and using it in future applications.

Answer 1

Order of multiplication between matrix and vector is not comutative, so
your vertex shader have to output Projection * Model * Vertex and not the opposite.

Answer 2

I solved the mystery of the undrawn lines by allocating more space to write vertex data in a different part of my code. As for my other problems, although the order of multiplication being done in my vertex shader was actually alright, I had messed up another fundamental concept of vector math. The dot product of two face normals will be a negative number when the normals make an obtuse angle... the way a sharp point on my model would. Also, there is the faulty logic above that basically says that if the face is visible, draw all of the lines on it. I re-wrote my shader to test first if a face was visible, and then in that same conditional block I did the test for sharp edges. Now, if a face is visible BUT it doesn't create a sharp edge, the shader will ignore that edge. Also, outlines appear now, just not perfectly. Here is a modified version of the above vertex shader:
uniform mat4 worldMatrix; /* the matrix that defines how to project a point from
object space to world space.*/
uniform mat4 viewProjMatrix; // the view (pertaining to screen size) matrix times the projection (how to project points to 3D) matrix.
uniform vec4 eyepos; // the position of the eye, given by the program.
attribute vec3 a; // one vertex on an edge, having an x,y,z, and w coordinate.
attribute vec3 b; // the other edge vertex.
attribute vec3 n1; // the normal of the face the edge is on.
attribute vec3 n2; // another normal in the case that an edge shares two faces... otherwise, this is the same as n1.
attribute float w; // an attribute given to make a binary choice between two edges when they draw on top of one another.
void main()
{
// WORLD SPACE ATTRIBUTES //
vec4 eye_world = eyepos * worldMatrix;
vec4 a_world = vec4(a.x, a.y,a.z,1.0) * worldMatrix;
vec4 b_world = vec4(b.x, b.y,b.z,1.0) * worldMatrix;
vec4 n1_world = normalize(vec4(n1.x, n1.y,n1.z,0.0) * worldMatrix);
vec4 n2_world = normalize(vec4(n2.x, n2.y,n2.z,0.0) * worldMatrix);
// END WORLD SPACE ATTRIBUTES //
// TEST CASE ATTRIBUTES //
float a_vertex = dot(eye_world - a_world, n1_world);
float b_vertex = dot(eye_world - b_world, n2_world);
float normalDot = dot(n1_world.xyz, n2_world.xyz);
float vertProduct = a_vertex * b_vertex;
float hardness = 0.0; // this would be the value for an object made of sharp angles, like a box. Take a look at its use below.
// END TEST CASE ATTRIBUTES //
gl_Position = vec4(2.0,2.0,2.0,1.0); // if all else fails, keeping this here will discard unwanted data.
if (vertProduct >= 0.1) // NOTE: face is behind the viewable portion of the object, normally uses 0.0 when not checking for silhouette
{
gl_Position = vec4(2.0,2.0,2.0,1.0);
}
else if(vertProduct < 0.1 && vertProduct >= -0.1) // NOTE: face makes almost a right angle with the eye vector
{
if(w == 0.0)
{
vec4 p = vec4(a_world.x, a_world.y, a_world.z, 1.0);
p = p * viewProjMatrix;
gl_Position = p;
}
else
{
vec4 p = vec4(b_world.x, b_world.y, b_world.z, 1.0);
p = p * viewProjMatrix;
gl_Position = p;
}
}
else // NOTE: this is the case where you can very clearly see a face.
{ // NOTE: the number that normalDot compares to should be its "hardness" value. The more negative the value, the smoother the surface.
// a.k.a. the less we care about hard edges (when the normals of the faces make an obtuse angle) on the object, the more negative
// hardness becomes on a scale of 0.0 to -1.0.
if(normalDot <= hardness) // NOTE: the dot product of the two normals is obtuse, so we are looking at a sharp edge.
{
if(w == 0.0)
{
vec4 p = vec4(a_world.x, a_world.y, a_world.z, 1.0);
p = p * viewProjMatrix;
gl_Position = p;
}
else
{
vec4 p = vec4(b_world.x, b_world.y, b_world.z, 1.0);
p = p * viewProjMatrix;
gl_Position = p;
}
}
else // NOTE: not sharp enough, just throw the vertex away
{
gl_Position = vec4(2.0,2.0,2.0,1.0);
}
}
}