A generative design system is proposed to produce distinct design variations from an example design supplied by users. The designs are represented using profile curves and generated under geometric rules. This system is useful for product aesthetic design, which is crucial for the global market that requires creativity under limited conditions such as manufacturing methods, cost, durability and so on. Since aesthetics must be combined with such conditions, designers must create many design alternatives and select the ones, which satisfy all defined requirements. Therefore, the conceptual design stage may take long time specifically when creative ideas are needed. The proposed approach can generate the design alternatives by minimum effort thanks to our easy to use system, where users only need to define points of the product profile by simply mouse-clicking on the product image. Once the points are supplied, the product profile curve is automatically defined using a composite cubic Bezier curve. It is modified to generate design variation under geometric constraints defined by geometric shapes such as circles, triangles and ellipses. Similarity measures, anisotropy ratio of the transformation of generated samples to the example profile and modified Hausdorff distance between the sample profiles, are used to constrain generating irrelevant samples to the example profile, but ensuring the generated samples are different enough from each other and from the example profile. All these constraints are used in the proposed search algorithm to explore the samples.