Resolution projection transformation
papers Posted: 2011-05-01 Paper Source: www.teachpaper.com papers published by: Teaching Teaching Papers Papers Hits: times parse projection transformation elective 4-2 second chapter describes the six common plane transformations, namely identity,
MBTシューズ 販売店, stretch pressure, reflection, rotation, projection, shear transformation, projection transformation here for some brief analysis. First, the projection transformation of conceptual knowledge comes from life, in fact, life in the projection of the shortage of examples. If the object in the solar irradiation produces a shadow that is cast resolution projection transformation
First,
ed hardy canada, the concept of projection transformation
knowledge comes from life, in fact, life in the projected shortage of examples. If the object in the solar irradiation produces a shadow,
replica oakley sunglasses, is the projection. So what is the projection transform it? I believe we have seen volleyball match it, the break, they both opposite garbage onto the mop in line l at the end. We can approximate the volleyball games as flat to the line l is the x-axis, O is the origin of the space center to establish the coordinate system, then dragged back and forth on the plane can be seen as a geometric transformation T: → =, then corresponding transformation matrix M = 1 00 0. Like this will be projected onto a plane straight line graph transformation is called projective transformations, while the corresponding projection matrix is called the transformation matrix. Here we find that projection transform is a linear transformation, while it was mapped, but not one mapping.
Second, several common projective transformation
1. will be projected on the plane perpendicular to the x-axis transformation
like mopping the floor in front of the example cited, M = 1 00 0 is the case. For example: the curve M = 1 00 0 in the matrix under the action of the corresponding projective transformation into what graphics? Analysis: Let P be the curve y = sinx at any point, it is transformed into a point after P ', then x'y' = 1 00 0xy = x0, ie y '= 0, ie, after the cross point of the transformed coordinates unchanged, the vertical axis to 0, so the curve along the x-axis perpendicular to the direction of projection to the x-axis, into a straight line y = 0.
2. the plane perpendicular to the y-axis projection transformation
not difficult to see such a transformation T: → =, the corresponding transformation matrix is 0001. For example: oval x2 + = 1 in the matrix 0001 corresponds to the transformation under the effect of drawing it into what? Resolution: Because the x'y '= 0 00 1xy = 0y, so x' = 0y '= y, that is transformed through the same point of the vertical axis, horizontal axis to 0, so the ellipse x2 + = 1 along the vertical y axis projected onto the y-axis, into a line x = 0.
3. to a point on the plane along the x-axis projected onto the line y = x on the transformation
we compare the two kinds of transformation matrix M1 = 1 01 0 and M2 = 0 10 1. For M1 the corresponding transformation T1: xy → x'y '= 1 01 0xy = xx, which transform the same horizontal, vertical and horizontal coordinates become equal, it is the plane of the points along the direction perpendicular to the x-axis projection to the straight line y = x on. For M2 the corresponding transformation T2: xy → x'y '= 0 10 1xy = yy, which transformed the same vertical axis, horizontal and vertical coordinates become equal, it is the plane perpendicular to the y-axis points along the direction of the projection to the line y = x on. By comparison we can see that though they are projected onto the line y = x, but different because the direction of projection, would lead to different results and different transformation matrix.
Third, some other projection transformations
above two points in the projection direction is perpendicular with the axis, let's explore some of the other conditions.
For example: Let a projective transformation to any point along the plane parallel to the straight line y = x the direction of the projection to the x-axis, find the A obtained under this transformation the coordinates of point A, and find the projection transformation corresponding transformation matrix.
Resolution: figure,
Oakley sunglasses sale, a straight line through point A parallel line y = x cross x-axis at point A ', then the straight line AA' of the equation: y-1 = x-2, so y = 0 then x = 1, so A '. Similarly, any point within the plane can be obtained, under this transformation into a point, that is, xy → xy 0 = 1 · x-1 · y0 · x +0 · y = 1-100xy, so the demand is a transformation matrix -100. Just think that if the title to any point along the plane parallel to the straight line y = x the direction of the projection to the y-axis, find the projection transformation, the transformation matrix corresponding to it? Easy to find the transformed point,
tods shoes outlet, that is, xy → 0y-x 0 · x +0 · y-1 · x +1 · y = 00-1 1xy, so the transformation matrix for the 00-11. Then imagine that if the title to any point along the plane perpendicular to the line y = x the direction of the projection to the line y = x, and find the corresponding transformation matrix projection transform it? Analysis: Let P be any point on the plane, it on the line y = x symmetry of the point P ', PP' perpendicular to the linear connection y = x, and the intersection of Q, then xy → = xy, so the transformation matrix is .
short, clear projection transformation key is to analyze the transformation of the coordinate transformation before and after the law, and the projection direction, which corresponds to the abstract transformation matrix.
Author: Huaian School
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