Yesterday I asked this question seems not clear. So, I am writing new question with mathematical terms only.
Here is some points about shapes I used:
- Square: Rectangle that all angles are 90° & all sides are equal length. So, consider Square also a Rectangle.
- Triangle: I used an equilateral triangle is a triangle in which all three sides have the same length.
- Polygon: A finite number of straight line segments connected to form a closed.
So, Here after I use the term Polygon to describe triangle & rectangle shapes when it's required to mention consider this shape as polygone
. Becuase, I used triangle (regular polygon) to simplfy the work to find out the formula.
Variables used in this problem:
- b = Border width
Bounds of Outer Rectangle (r) that enclosing the polygon(p):
- x = Origin x
- y = Origin y
- w = Width
- h = Height
So, If r = (x,y,w,h)
then, Bounds of Inner Rectangle that encloses the inner polygon(p1) (r1) = (x1,y1,w1,h1)
Here, inner polygon = Polygon by subtracting the border width.
What is my final goal:
I should able to calculate inner rectangle boundary of any polygon like below image, I have angles, outer rectangle bounds & border width. The problem is to find out the inner rectangle bounds across to the outer rectangle based on the polygon at that enclosed by inner rectangle.
Problem 1:
Consider a Polygon(p) as a shape of rectangle(r) which has width(w) is 100 & height(h) is 100. The border width of the polygon is 10. The what is the inner boundary of the rectangle that encloses the inner polygon?
Note: I solved it by mind calculation(I didn't took angles in the calculation). But we can't apply this same formula for triangle. So, this is not solution for my problem.
Problem 2:
Consider the polygon (don't consider regulard) with three edges and three vertices & all angles are equal in measure.
If the rectangle(r) boundary is zero & size(w,h) is (100,87) that encloses the polygon(p) along with polygon border width as 10, then
What is the bounds of the inner rectangle(r2) that encloses the inner polygon(p2) ?
Hope I clearly explained the problem. If anything I am missed then please let me know. Thanks in advance.