How to build perspective projection matrix (no API)

Question

I develop a simple 3D engine (Without any use of API), successfully transformed my scene into world and view space but have trouble projecting my scene (from view space) usi

Answer 1

Following is a typical implemenation of perspective projection matrix. And here is a good link to explain everything OpenGL Projection Matrix

void ComputeFOVProjection( Matrix& result, float fov, float aspect, float nearDist, float farDist, bool leftHanded /* = true */ )
{
    //
    // General form of the Projection Matrix
    //
    // uh = Cot( fov/2 ) == 1/Tan(fov/2)
    // uw / uh = 1/aspect
    // 
    //   uw         0       0       0
    //    0        uh       0       0
    //    0         0      f/(f-n)  1
    //    0         0    -fn/(f-n)  0
    //
    // Make result to be identity first

    // check for bad parameters to avoid divide by zero:
    // if found, assert and return an identity matrix.
    if ( fov <= 0 || aspect == 0 )
    {
        Assert( fov > 0 && aspect != 0 );
        return;
    }

    float frustumDepth = farDist - nearDist;
    float oneOverDepth = 1 / frustumDepth;

    result[1][1] = 1 / tan(0.5f * fov);
    result[0][0] = (leftHanded ? 1 : -1 ) * result[1][1] / aspect;
    result[2][2] = farDist * oneOverDepth;
    result[3][2] = (-farDist * nearDist) * oneOverDepth;
    result[2][3] = 1;
    result[3][3] = 0;
}

Answer 2

Another function that may be useful.

This one is based on left/right/top/bottom/near/far parameters (used in OpenGL):

static void test(){
    float projectionMatrix[16];

    // width and height of viewport to display on (screen dimensions in case of fullscreen rendering)
    float ratio = (float)width/height;
    float left = -ratio;
    float right = ratio;
    float bottom = -1.0f;
    float top = 1.0f;
    float near = -1.0f;
    float far = 100.0f;

    frustum(projectionMatrix, 0, left, right, bottom, top, near, far);

}

static void frustum(float *m, int offset,
                     float left, float right, float bottom, float top,
                     float near, float far) {

    float r_width  = 1.0f / (right - left);
    float r_height = 1.0f / (top - bottom);
    float r_depth  = 1.0f / (far - near);
    float x =  2.0f * (r_width);
    float y =  2.0f * (r_height);
    float z =  2.0f * (r_depth);
    float A = (right + left) * r_width;
    float B = (top + bottom) * r_height;
    float C = (far + near) * r_depth;
    m[offset + 0] = x;
    m[offset + 3] = -A;
    m[offset + 5] = y;
    m[offset + 7] = -B;
    m[offset + 10] = -z;
    m[offset + 11] = -C;
    m[offset +  1] = 0.0f;
    m[offset +  2] = 0.0f;
    m[offset +  4] = 0.0f;
    m[offset +  6] = 0.0f;
    m[offset +  8] = 0.0f;
    m[offset +  9] = 0.0f;
    m[offset + 12] = 0.0f;
    m[offset + 13] = 0.0f;
    m[offset + 14] = 0.0f;
    m[offset + 15] = 1.0f;

}