1. A computer-implemented method for projecting a texture map onto a three-dimensional (3D) model, the method comprising: generating a polyline that includes a first plurality of points that resides along a stroke path defined across a surface region of the 3D model; generating a geodesic trace that includes a second plurality of points that resides within a threshold distance of the polyline; generating a UV coordinate for each point included in the first plurality of points and for each point included in the second plurality of points; and projecting the texture map onto the surface region of the 3D model according to the UV coordinates for each point included in the first plurality of points and the UV coordinates for each point included in the second plurality of points.