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 | 1 | initial version |
Linear transformation can be represented as matrix. Assume that you have an object that is set of points, each in the form of p=(x,y). If you want apply rotation, scaling or shear to it, you just need to find 2x2 matrix A, and for each point p calculate A*p. Result is rotated and scaled object. But some of extreamely frequent operations are not linear transformation. Shift for example. Or projective transformation. As a result you can't describe them as matrix operation. Homogeneous coordinates is a workaround for this problem. Instead of represnting point as (x,y) you represent it as (x,y,1). Now you can store those transformations as 3x3 matrix B (that part of it is 1 and 0).
| | 2 | No.2 Revision |
Linear transformation can be represented as matrix. Assume that you have an object that is set of points, each in the form of p=(x,y). If you want to apply rotation, scaling or shear to it, you just need to find 2x2 matrix A, and for each point p calculate A*p. Result As a result objected is rotated rotated, scaled and scaled object. sheared. But some of extreamely frequent operations transformations are not linear transformation. linear. Shift for example. Or projective transformation. As a result you can't describe them as matrix operation. Homogeneous coordinates is a workaround for this problem. Instead of represnting point as (x,y) you represent it as (x,y,1). Now you can store those transformations as 3x3 matrix B (that part of it is 1 and 0).
