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POOptimizing a pinhole camera rendering system
 

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  1. POOptimizing a pinhole camera rendering system
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    <p>I'm making a software rasterizer for school, and I'm using an unusual rendering method instead of traditional matrix calculations. It's based on a <a href="http://en.wikipedia.org/wiki/Pinhole_camera_model" rel="nofollow noreferrer">pinhole camera</a>. I have a few points in 3D space, and I convert them to 2D screen coordinates by taking the distance between it and the camera and normalizing it</p> <pre><code>Vec3 ray_to_camera = (a_Point - plane_pos).Normalize(); </code></pre> <p>This gives me a directional vector towards the camera. I then turn that direction into a ray by placing the ray's origin on the camera and performing a ray-plane intersection with a plane slightly behind the camera.</p> <pre><code>Vec3 plane_pos = m_Position + (m_Direction * m_ScreenDistance); float dot = ray_to_camera.GetDotProduct(m_Direction); if (dot &lt; 0) { float time = (-m_ScreenDistance - plane_pos.GetDotProduct(m_Direction)) / dot; // if time is smaller than 0 the ray is either parallel to the plane or misses it if (time &gt;= 0) { // retrieving the actual intersection point a_Point -= (m_Direction * ((a_Point - plane_pos).GetDotProduct(m_Direction))); // subtracting the plane origin from the intersection point // puts the point at world origin (0, 0, 0) Vec3 sub = a_Point - plane_pos; // the axes are calculated by saying the directional vector of the camera // is the new z axis projected.x = sub.GetDotProduct(m_Axis[0]); projected.y = sub.GetDotProduct(m_Axis[1]); } } </code></pre> <p>This works wonderful, but I'm wondering: can the algorithm be made any faster? Right now, for every triangle in the scene, I have to calculate three normals. </p> <pre><code>float length = 1 / sqrtf(GetSquaredLength()); x *= length; y *= length; z *= length; </code></pre> <p>Even with a fast reciprocal square root approximation (<code>1 / sqrt(x)</code>) that's going to be very demanding.</p> <p>My questions are thus:<br> Is there a good way to approximate the three normals?<br> What is this rendering technique called?<br> Can the three vertex points be approximated using the normal of the centroid? ((v0 + v1 + v2) / 3)</p> <p>Thanks in advance.</p> <p>P.S. "You will build a fully functional software rasterizer in the next seven weeks with the help of an expert in this field. Begin." I ADORE my education. :)</p> <p><strong>EDIT:</strong></p> <pre><code>Vec2 projected; // the plane is behind the camera Vec3 plane_pos = m_Position + (m_Direction * m_ScreenDistance); float scale = m_ScreenDistance / (m_Position - plane_pos).GetSquaredLength(); // times -100 because of the squared length instead of the length // (which would involve a squared root) projected.x = a_Point.GetDotProduct(m_Axis[0]).x * scale * -100; projected.y = a_Point.GetDotProduct(m_Axis[1]).y * scale * -100; return projected; </code></pre> <p>This returns the correct results, however the model is now independent of the camera position. :(</p> <p>It's a lot shorter and faster though!</p>
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    1. CONice to see fellow IGAD students over here as well :-)
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      1. USJasper Bekkers
    2. COThe pin hole camera model is often implemented using matrix calculations with homogenous coordinates. So why are you not using that?
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      1. USHannes Ovrén
 

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