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可以解释为,同一点M在旧坐标系xoy中的坐标(x,y)和它在新坐标系x_1o_1y_1中的坐标(x_1,y_1)之间的联系。其中a,b是新坐标系原点o_1在旧坐标系中的坐标,而θ新坐标轴o_1x_1由ox方向开始的转动角。这时,由于新旧坐标系是相对固定的,所以a,b,θ皆为常数。 如果我们只考虑一个固定的点M,则公式(1)给出的是两组定数(x_1,y_1)和(x,y)之间的关系。如果把点M看做是某曲线上的任意点,则公式(1)(或其反变换)给出了一条曲线在两个坐标系中的方程之间变形公式。
It can be interpreted as the relation between the coordinate (x, y) of the same point M in the old coordinate system xoy and its coordinate (x_1, y_1) in the new coordinate system x_1o_1y_1. Where a and b are the coordinates of the origin of the new coordinate system o_1 in the old coordinate system and θ is the rotation angle of the new axis o_1x_1 from the ox direction. At this moment, a, b, θ are all constant because the old and new coordinate systems are relatively fixed. If we consider only a fixed point M, then the formula (1) gives the relationship between the two sets of fixed numbers (x_1, y_1) and (x, y). If we regard point M as an arbitrary point on a curve, then equation (1) (or its inverse transform) gives a formula for the deformation of the equation between the two coordinate systems.