GeoText: Geodesic-Based 3D Text Generation on Triangular Meshes

Embedding text on 3D triangular meshes is essential for conveying semantic information and supporting reliable identification and authentication. However, existing methods often fail to incorporate the geometric properties of the underlying mesh, resulting in shape inconsistencies and visual artifacts, particularly in regions with high curvature. To overcome these limitations, we present GeoText, a framework for generating 3D text directly on triangular meshes while faithfully preserving local surface geometry. In our approach, the control points of TrueType Font outlines are mapped onto the mesh along a user-specified placement curve and reconstructed using geodesic Bézier curves. We introduce two mapping strategies—one based on a local tangent frame and another based on straightest geodesics—that ensure natural alignment of font control points. The reconstructed outlines enable the generation of embossed, engraved, or independent 3D text meshes. Unlike Boolean-based methods, which combine text meshes through union or difference and therefore fail to lie exactly on the surface—breaking the symmetry between embossing and engraving—our offset-based approach ensures a symmetric relation: positive offsets yield embossing, whereas negative offsets produce engraving. Furthermore, our method achieves robust text generation without self-intersections or inter-character collisions. These capabilities make GeoTextwell suited for applications such as 3D watermarking, visual authentication, and digital content creation.