Formgeometry

Formgeometry is an interdisciplinary field that studies the properties and relationships of geometric forms, with an emphasis on form as an entity independent of metric measurements. It investigates how shapes appear, transform, and relate to one another through operations such as morphing, deformation, symmetry, and subdivision. Unlike traditional Euclidean geometry, which centers on exact distances, formgeometry foregrounds qualitative features such as silhouette, topology, and structural invariants.

Core concepts include form, shape, and the space of shapes (shape space), as well as equivalence under transformations and invariants under morphisms. The field analyzes how forms can be classified, compared, and evolved through controlled deformations. Methods often combine computational geometry, shape analysis, and variational techniques, using representations such as meshes, splines, and point clouds to describe form. Theoretical foundations are drawn from differential geometry, algebraic topology, and graph theory to describe continuous and discrete changes in form.

Applications span computer-aided design, computer graphics, architectural analysis, digital fabrication, and animation. Formgeometry provides tools to compare shapes, design smooth transitions between forms, and assess qualitative aspects of aesthetics, balance, or structural behavior beyond exact measurements.

History and development: the term formgeometry has appeared in design and mathematics literature as a bridge between formal geometry and form-driven design. It emerged from interests in object recognition, morphable models, and shape spaces, and continues to evolve with advances in 3D scanning, machine learning for shape analysis, and immersive visualization.

See also: geometry, topology, computational geometry, shape analysis, morphing, computer-aided design.