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Scratchpad was a constraint-based graphics system.

What does it mean by a Constraint-based Graphics System?

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If you have a geometric drawing with measurements you can solve what the shape has to be. This is valuable for example in engineering as it allows you specify the requirements and the computer can then solve the constrained drawing via a solver.

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Image 1: Constraint solver in action, red constraints are fixed while blue ones are free to change.

There are several ways how the solver might work, it could be a numeric nonlinear based on gradient descent. Or it can be fully algebraic. Usually its a gradient descent solver as this is easier to implement, and possibly faster.

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Sketchpad was a system that allowed you to draw simple shapes using lines and curves in 2D. It maintained constraints between the shapes. For example, an endpoint of one line could be constrained to lie on another line. Also, as mentioned in the Wikipedia article, the user could set a fixed length for a line, or an angle between two connected lines. These constraints would be automatically applied by the system while editing the diagrams—e.g., when moving one line, other lines would be adjusted to maintain the constraints.

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