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We propose a new sketch parsing and beautification method that converts digitally created design sketches into beautified line drawings. Our system uses a trainable, sequential bottom-up and top-down stroke clustering method that learns how to parse input pen strokes into groups of strokes each representing a single curve, followed by point-cloud ordering that facilitates curve fitting and smoothing. This approach enables greater conceptual freedom during visual ideation activities by allowing designers to develop their sketches using multiple, casually drawn strokes without requiring them to indicate the separation between different stroke groups. With the proposed method, raw sketches are seamlessly converted into vectorized geometric models, thus, facilitating downstream assessment and editing activities.