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mathgeometrytransformationbounding-box

Get the bounding box of a sheared and rotated rectangle

I can get the bounding box of sheared or rotated rectangle using this formula

shearedW = Abs(Tan(shearX) * Height) + Width
shearedH = Abs(Tan(shearY) * Width) + Height
rotatedW = Abs(Cos(angle) * Width) + Abs(Sin(angle) * Height)
rotatedH = Abs(Sin(angle) * Width) + Abs(Cos(angle) * Height)

But how to combine those? I just need to know the width and height. The transformation is done by shearing then rotating the shape.

Solution

  • Just build affine matrix for combined transformation and apply it to vertices, then get differences for y- and x- coordinates.

    Note that first pair of formulas is wrong - it gives additional width and heght. Full width:

    shearedW =  Width + Abs(Tan(shearX) * Height)