P' = P*M is the coordinator of the point after the operation.Ī sequence of operation can also be composed to be one operation. Representation of translating the object a blocks right, b blocks up and cīlocks forward, then after the translating, the point's coordinator will become The operation, and M = (1 0 0 a)(0 1 0 b)(0 0 1 c) (0 0 0 1) is the matrix For example, P = (x, y, z, 1) is a point's coordinator before ![]() By multiplying the matrix, a vector/point can be transformedīy the operation. Matrix implementation is a powerful technique used for computer graphics.įor the concerns stated in section II, matrix for 3D space is representedĮach operation of object such as translation and rotation can be representedīy one Matrix. Take a look of the source code for detailed if the last element is "0": Result is a Vector.if the last element is "1": Result is a Point.Implemented by performing the corresponding arithmetic operation on their Therefore, you can see the nice property about this particular representation.Įvery legal operation to be performed on points and vectors, can be These operation can also be checked if using We know that if a point subtracting a point will become a vector, a vectorĪdd a scale will still be a vector. There is no way to distinguish them.Ī better way to do it is to append an extra element at the end of the array.įor scalers, the 4th element will be 1, for vectors, the 4th element will be 0.įor example, A = (x, y, z, 0) indicates that A is a vector, and B = (x, y, z, 1) For example, give an object A = (x, y, z), this object A could beĮither a point at (x, y, z) position or a vector that points to (x, y, z)ĭirection. ![]() ![]() However, this is a subtle way to representĪ 3D space. Since this is for 3D space, each point/vector should have 3 element, one forĮach direction of the 3D space. Transformation, 3D Volumn Clipping, Hidden Surface/Line Removal and Ray Tracing. Such techniques include Coordinator Frame Transformation, Perspective These techniques are used to implement my 3D animation program written in This paper describes several techniques used in 3D graphics implementation. 3D Graphics Implementation 3D Graphics Animation in Computer Graphics by Connie K.
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