Techniques for improving efficiency and accuracy of computer-aided design are provided. In one aspect, a method for generating a computer-based representation of a design having one or more shapes is provided comprising the following steps. Each of the shapes in the design is represented with one or more trapezoids, wherein a fixed number of non-vertical lines are used to define an x-coordinate of a left and right base and sides of each trapezoid with intersection points being formed between the non-vertical lines that define the sides. The x-coordinates and intersection points are used to divide the trapezoids into disjoint trapezoids, wherein each disjoint trapezoid is defined by a combination of the same non-vertical lines that are used to define one or more of the trapezoids. An order is assigned to the x-coordinates and intersection points, wherein the x-coordinates and intersection points in the assigned order are representative of the design.