If I want to expand or reduce a shape what mathematical methods are there to do this.
I'd like to understand scaling which seems simple enough. Using my limited knowledge I would do this by measuring the angle and distance of each point from a given anchor point, and then re-plot them by multiplying the distance against a scaling factor.
I have no idea how optimal this method is, or how to express it using mathematical notation, so I'd like to know.
I'd also very much like to understand how to make a shape expand or reduce around it's interior. For example, I thought it would be something like this...
I use a circle of a given radius on each point, and at each point create a bisecting line, then construct the larger or smaller shape using the intersecting points of the circles. However, as you can see this method has numerous errors, shape B obviously has angles that differ from shape A, what's the correct way to expand / shrink a shape in this manner?
Plain english and mathematical notation answers are gratefully requested, I'm still learning a lot of notation.
I'm not sure that the second example is clear enough, so I've made this image to describe what I'm looking for.
Using this example, it's clear that projection scaling isn't going to produce the shape required. what is this sizing method called, and how is it done mathematically?
Answer
You can follow your anchor point (projection) approach using a point in the interior. That will preserve angles. It is not clear how you got from A to B in the second drawing. The lines between corresponding vertices do not meet in a point, which is why the angles change.
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