The generic scaling matrix looks like this: Pretty simple.Ī scaling matrix takes a vector or set of vectors, and expands or reduces it along one or more of the two dimensions, x and y. The dotted black square is formed from translating the ends of those vectors one unit to the right: (2, 1), (0, 1), (0,-1) and (2,-1). The figure below shows the square (pink) formed by vectors (1, 1), (-1, 1), (-1,-1) and (1,-1). These are really just sums and differences of vectors, and here we only care about the locations of the pointed ends. The second scenario is when vectors describe the vertices or special points of some figure. We do translations like this all the time to manipulate vectors numerically. We actually need to subtract 2 from the x coordinates of both the origin (0, 0) and the tip of vector (2, 2), which gives us the properly-translated vector on the left. If we want to translate just that vector two units to the left, it's not enough to subtract 2 from the x-coordinate of (2, 2), which would give us the vector (0, 2), which doesn't have the same direction (slope) as (2, 2). The figure below shows vector (2, 2) extending from the origin (vector on the right). We have to be careful about what we are translating. Oddly, translation is perhaps the least straightforward operation on vectors in terms of the geometry. Translation of a 2-D vector is done by adding a constant value to its x and/or y coordinate(s).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |