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Virtual Cameras

 How To Make A Virtual Camera Viewing System

 Written by Written by Stelios/Scoopex ([email protected]) HTML-Version by Azure Introduction The following algorithms describe how to create a "virtual camera" viewing system in which you have a camera positioned anywhere in a 3D world pointing to an arbitrary focus point. Camera Z panning (roll) is also possible by defining a direction vector. Equations ```O = observer position (camera) A = aimpoint position (focus) R = direction point position (up) N = normalize (Ax - Ox, Ay - Oy, Az - Oz) D = normalize (Rx - Ox, Ry - Oy, Rz - Oz) V = D - (D . N) * N U = cross product (V,N) | Ux Uy Uz | View Matrix = | Vx Vy Vz | | Nx Ny Nz | ``` Before rotating, you must translate all points so that their origin is point A ; after rotating you must translate the Z offsets using the distance from point O to A, ie. the length of the N vector before normalizing. Note that "." means dot product and "*" means multiplying each component of the N vector with the dot product. (scalar / vector multiplication) Hints If you wish to specify the angle for camera Z panning yourself: a = angle for camera Z-panning (roll) D = [sin(a), cos(a), 0] You must take care of the special case O=A ; don't alter the view matrix and use the previous one. If O=A happens at the first drawing frame and you don't have a previous view matrix use this instead: ``` | 1 0 0 | View Matrix = | 0 1 0 | | 0 0 1 | ``` You must take care of the special case where vector N is parallel to vector D, ie. abs(D.N) = 1. I have solved this special case by rolling the components of D like this: D = (Dz, Dx, Dy) Another special case is when O=R ; there will be no D then. In this case either use previous D or create a fixed one: D = (0, 1, 0) This is, of course, not needed if you specify D yourself (see above). In theory, vectors U & V don't need normalizing but it is advised to normalize those if you are using fixed point math instead of floats in order to avoid overflows caused by precision errors. Final words I use the above algorithms in my 3D engine and they work perfectly. Thanks must go to Silver Eagle/Pygmy Projects, Celebrandil/Phenomena and Scout/C-Lous for their (kind) support.

Last change: 16.01.2001