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POMatrix transformations to recreate camera "Look At" functionality
 

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  1. POMatrix transformations to recreate camera "Look At" functionality
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    <p><strong>Summary:</strong></p> <p>I'm given a series of points in 3D space, and I want to analyze them from any viewing angle. I'm trying to figure out how to reproduce the "Look At" functionality of OpenGL in WPF. I want the mouse move X,Y to manipulate the Phi and Theta Spherical Coordinates (respectively) of the camera so that I as I move my mouse, the camera appears to orbit around the center of mass (generally the origin) of the point cloud, which will represent the target of the Look At</p> <p><strong>What I've done:</strong></p> <p>I have made the following code, but so far it isn't doing what I want:</p> <pre><code> internal static Matrix3D CalculateLookAt(Vector3D eye, Vector3D at = new Vector3D(), Vector3D up = new Vector3D()) { if (Math.Abs(up.Length - 0.0) &lt; double.Epsilon) up = new Vector3D(0, 1, 0); var zaxis = (at - eye); zaxis.Normalize(); var xaxis = Vector3D.CrossProduct(up, zaxis); xaxis.Normalize(); var yaxis = Vector3D.CrossProduct(zaxis, xaxis); return new Matrix3D( xaxis.X, yaxis.X, zaxis.X, 0, xaxis.Y, yaxis.Y, zaxis.Y, 0, xaxis.Z, yaxis.Z, zaxis.Z, 0, Vector3D.DotProduct(xaxis, -eye), Vector3D.DotProduct(yaxis, -eye), Vector3D.DotProduct(zaxis, -eye), 1 ); } </code></pre> <p>I got the algorithm from this link: <a href="http://msdn.microsoft.com/en-us/library/bb205342(VS.85).aspx" rel="nofollow">http://msdn.microsoft.com/en-us/library/bb205342(VS.85).aspx</a></p> <p>I then apply the returned matrix to all of the points using this:</p> <pre><code> var vector = new Vector3D(p.X, p.Y, p.Z); var projection = Vector3D.Multiply(vector, _camera); // _camera is the LookAt Matrix if (double.IsNaN(projection.X)) projection.X = 0; if (double.IsNaN(projection.Y)) projection.Y = 0; if (double.IsNaN(projection.Z)) projection.Z = 0; return new Point( (dispCanvas.ActualWidth * projection.X / 320), (dispCanvas.ActualHeight * projection.Y / 240) ); </code></pre> <p>I am calculating the center of all the points as the <code>at</code> vector, and I've been setting my initial <code>eye</code> vector at <code>(center.X,center.Y,center.Z + 100)</code> which is plenty far away from all the points</p> <p>I then take the mouse move and apply the following code to get the Spherical Coordinates and put that into the <code>CalculateLookAt</code> function:</p> <pre><code> var center = GetCenter(_points); var pos = e.GetPosition(Canvas4); //e is of type MouseButtonEventArgs var delta = _previousPoint - pos; double r = 100; double theta = delta.Y * Math.PI / 180; double phi = delta.X * Math.PI / 180; var x = r * Math.Sin(theta) * Math.Cos(phi); var y = r * Math.Cos(theta); var z = -r * Math.Sin(theta) * Math.Sin(phi); _camera = MathHelper.CalculateLookAt(new Vector3D(center.X * x, center.Y * y, center.Z * z), new Vector3D(center.X, center.Y, center.Z)); UpdateCanvas(); // Redraws the points on the canvas using the new _camera values </code></pre> <p><strong>Conclusion:</strong></p> <p>This does not make the camera orbit around the points. So either my understanding of how to use the Look At function is off, or my math is incorrect.</p> <p>Any help would be very much appreciated.</p>
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    1. CODon't involve the mouse yet, just try some values for `theta` and `phi`. Does (0, 0) work? How about (0, 0.1)? (0.1, 0)?...
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