Question

我有一块方板。我希望它在圆角方框内。问题似乎是基本的，但是你如何计算你需要添加到方板的长度，以便制作一个具有特定半径的圆角方框来完全覆盖它？

例如我有一个正方形30x30mm板，我想用一个方圆框覆盖它，其角半径为6mm，我必须添加多长度30mm 1}}，创建那个盒子，这样它就可以填满原来的板子（所以板子可以准确地＃34;生活＆＃34;在那个盒子里面）

Answer 1

同意OP应用程序可能是木工，但它似乎是一个有趣的几何问题，它可能有编程/图形应用程序。这就是我想出的：

Let I = inner square side length (30mm)
    O = outer rounded square side length
    r = corner radius (6mm)

Decompose the outer rounded square into 9 sections:
    1 center square (with diagonal length d and side length c)
    4 side squares (left, right, above, and below)
    4 round corners

Since the inner square fits into the outer square,
the outer rounded square diagonal is I * sqrt(2)

Since there are 2 rounded corners the diagonal of the center square is
    d = I sqrt(2) - 2 * r

The diagonal of the center square is sqrt(2) times its side
    d = c * sqrt(2)

Equating these two
    c = I - r * sqrt(2)

The side length of the outer square is
    O = c + 2 * r

Substituting for c
    O = I + r * (2 - sqrt(2))

您的问题要求添加的长度为

length to add = O - I = r * (2 - sqrt(2))

在你的情况下，6mm *（2 - sqrt（2））= 3.515mm （大约）

如何计算特定角半径的矩形尺寸？

1 个答案: