Approximation with a hybrid DD Stancu operator: Applications to coronary vessel visualization, image representation, and geometric modeling

This study presents a generalization of the DD Stancu operator reported in the literature by combining it with the lambda Bernstein operator. Using the basis functions of the proposed operator, geometric modeling applications related to vascular visualization, botanical form representation, and entomological form modeling are presented; thus, the role of approximation theory in mathematical modeling and the aforementioned fields is emphasized. The biological modeling and botanical illustration generated using the basis functions of the operator demonstrate the effectiveness of the method in representing organic shapes by enabling the λ-parameter to capture with high precision the natural forms of leaves and butterflies, their internal curves, and venation structures. The model, developed to represent structural changes such as narrowing and widening in vascular geometry, was designed solely as a geometric visualization tool rather than as a validated medical simulation or diagnostic method, and is made available for further studies.