Need help with implementing collision detection using the Separating Axis Theorem

Question

So, after hours of Googling and reading, I've found that the basic process of detecting a collision using SAT is:

for each edge of poly A
    project A and B onto the normal for this edge
    if intervals do not overlap, return false
end for

for each edge of poly B
    project A and B onto the normal for this edge
    if intervals do not overlap, return false
end for

However, as many ways as I try to implement this in code, I just cannot get it to detect the collision. My current code is as follows:

for (unsigned int i = 0; i < asteroids.size(); i++) {
    if (asteroids.valid(i)) {
        asteroids[i]->Update();

        // Player-Asteroid collision detection
        bool collision = true;
        SDL_Rect asteroidBox = asteroids[i]->boundingBox;

        // Bullet-Asteroid collision detection
        for (unsigned int j = 0; j < player.bullets.size(); j++) {
            if (player.bullets.valid(j)) {
                Bullet b = player.bullets[j];

                collision = true;
                if (b.x + (b.w / 2.0f) < asteroidBox.x - (asteroidBox.w / 2.0f)) collision = false;
                if (b.x - (b.w / 2.0f) > asteroidBox.x + (asteroidBox.w / 2.0f)) collision = false;
                if (b.y - (b.h / 2.0f) > asteroidBox.y + (asteroidBox.h / 2.0f)) collision = false;
                if (b.y + (b.h / 2.0f) < asteroidBox.y - (asteroidBox.h / 2.0f)) collision = false;

                if (collision) {
                    bool realCollision = false;

                    float min1, max1, min2, max2;

                    // Create a list of vertices for the bullet
                    CrissCross::Data::LList<Vector2D *> bullVerts;
                    bullVerts.insert(new Vector2D(b.x - b.w / 2.0f, b.y + b.h / 2.0f));
                    bullVerts.insert(new Vector2D(b.x - b.w / 2.0f, b.y - b.h / 2.0f));
                    bullVerts.insert(new Vector2D(b.x + b.w / 2.0f, b.y - b.h / 2.0f));
                    bullVerts.insert(new Vector2D(b.x + b.w / 2.0f, b.y + b.h / 2.0f));
                    // Create a list of vectors of the edges of the bullet and the asteroid
                    CrissCross::Data::LList<Vector2D *> bullEdges;
                    CrissCross::Data::LList<Vector2D *> asteroidEdges;
                    for (int k = 0; k < 4; k++) {
                        int n = (k == 3) ? 0 : k + 1;
                        bullEdges.insert(new Vector2D(bullVerts[k]->x - bullVerts[n]->x,
                                                bullVerts[k]->y - bullVerts[n]->y));
                        asteroidEdges.insert(new Vector2D(asteroids[i]->vertices[k]->x - asteroids[i]->vertices[n]->x,
                                                    asteroids[i]->vertices[k]->y - asteroids[i]->vertices[n]->y));
                    }

                    Vector2D *vectOffset = new Vector2D(asteroids[i]->center.x - b.x, asteroids[i]->center.y - b.y);

                    for (unsigned int k = 0; k < asteroidEdges.size(); k++) {
                        Vector2D *axis = asteroidEdges[k]->getPerpendicular();
                        axis->normalize();
                        min1 = max1 = axis->dotProduct(asteroids[i]->vertices[0]);
                        for (unsigned int l = 1; l < asteroids[i]->vertices.size(); l++) {
                            float test = axis->dotProduct(asteroids[i]->vertices[l]);
                            min1 = (test < min1) ? test : min1;
                            max1 = (test > max1) ? test : max1;
                        }
                        min2 = max2 = axis->dotProduct(bullVerts[0]);
                        for (unsigned int l = 1; l < bullVerts.size(); l++) {
                            float test = axis->dotProduct(bullVerts[l]);
                            min2 = (test < min2) ? test : min2;
                            max2 = (test > max2) ? test : max2;
                        }
                        float offset = axis->dotProduct(vectOffset);
                        min1 += offset;
                        max1 += offset;
                        delete axis; axis = NULL;
                        float d0 = min1 - max2;
                        float d1 = min2 - max1;
                        if ( d0 > 0 || d1 > 0 ) {
                            realCollision = false;
                            break;
                        } else {
                            realCollision = true;
                        }
                    }

                    if (realCollision) {
                        for (unsigned int k = 0; k < bullEdges.size(); k++) {
                            Vector2D *axis = bullEdges[k]->getPerpendicular();
                            axis->normalize();
                            min1 = max1 = axis->dotProduct(asteroids[i]->vertices[0]);
                            for (unsigned int l = 1; l < asteroids[i]->vertices.size(); l++) {
                                float test = axis->dotProduct(asteroids[i]->vertices[l]);
                                min1 = (test < min1) ? test : min1;
                                max1 = (test > max1) ? test : max1;
                            }
                            min2 = max2 = axis->dotProduct(bullVerts[0]);
                            for (unsigned int l = 1; l < bullVerts.size(); l++) {
                                float test = axis->dotProduct(bullVerts[l]);
                                min2 = (test < min2) ? test : min2;
                                max2 = (test > max2) ? test : max2;
                            }
                            float offset = axis->dotProduct(vectOffset);
                            min1 += offset;
                            max1 += offset;
                            delete axis; axis = NULL;
                            float d0 = min1 - max2;
                            float d1 = min2 - max1;
                            if ( d0 > 0 || d1 > 0 ) {
                                realCollision = false;
                                break;
                            } else {
                                realCollision = true;
                            }
                        }
                    }
                    if (realCollision) {
                        player.bullets.remove(j);

                        int numAsteroids;
                        float newDegree;
                        srand ( j + asteroidBox.x );
                        if ( asteroids[i]->degree == 90.0f ) {
                            if ( rand() % 2 == 1 ) {
                                numAsteroids = 3;
                                newDegree = 30.0f;
                            } else {
                                numAsteroids = 2;
                                newDegree = 45.0f;
                            }
                            for ( int k = 0; k < numAsteroids; k++)
                                asteroids.insert(new Asteroid(asteroidBox.x + (10 * k), asteroidBox.y + (10 * k), newDegree));
                        }
                        delete asteroids[i];
                        asteroids.remove(i);
                    }
                    while (bullVerts.size()) {
                        delete bullVerts[0];
                        bullVerts.remove(0);
                    }
                    while (bullEdges.size()) {
                        delete bullEdges[0];
                        bullEdges.remove(0);
                    }
                    while (asteroidEdges.size()) {
                        delete asteroidEdges[0];
                        asteroidEdges.remove(0);
                    }

                    delete vectOffset; vectOffset = NULL;
                }
            }
        }
    }
}

bullEdges is a list of vectors of the edges of a bullet, asteroidEdges is similar, and bullVerts and asteroids[i].vertices are, obviously, lists of vectors of each vertex for the respective bullet or asteroid.

Honestly, I'm not looking for code corrections, just a fresh set of eyes.

Answer 1

Turns out my mathematical understanding of the theorem was perfectly fine. Instead, the problem lay in the fact that I was not including the center points of the polygons in the vertice vectors.

Thank you everyone for their time.