如何计算圆的圆周上的点的(x或y)坐标?
问题描述：
px和py是圆圆周上的点的x和y坐标.
px and py are the x and y coordinates of a point on a circle's circumference.
给出:
the center of the circle as: cx, cy
the radius of the circle as: r
px
如何计算py的值?谢谢！
答
给出px，py最多有两个可能的值.
Given px there are at most two possible values for py.
看看勾股定理:(px-cx)^ 2 +(py-cy)^ 2 = r ^ 2.
Look at the pythagorean theorem: (px-cx)^2+(py-cy)^2=r^2.
让d = r ^ 2-(px-cx)^ 2
Let d=r^2-(px-cx)^2
如果d> 0，那么您有两个解决方案.得出py = sqrt(d)+ cy，其中平方根为正或负.
If d>0 then you have two solutions. This gives py=sqrt(d)+cy, where the square root is positive or negative.
如果d = 0，则您有一个解py = cy，即圆的左侧或右侧，具体取决于px
If d=0 then you have one solution py=cy, the left or right of the circle, depending on px
如果d
If d<0 you have no real points.