Progressive meshes (PM) are a new representation for storing and transmitting arbitrary triangle meshes. This paper introduces PM, which provides an efficient, lossless, continuous-resolution representation that addresses several practical problems in computer graphics, including smooth geomorphing of level-of-detail (LOD) approximations, progressive transmission, mesh compression, and selective refinement. The PM representation is constructed by simplifying a mesh through a sequence of edge collapse transformations, followed by a sequence of inverse vertex split transformations. This results in a continuous sequence of meshes of increasing accuracy, from which LOD approximations of any desired complexity can be efficiently retrieved. Moreover, geomorphs can be efficiently constructed between any two such meshes. The PM representation also naturally supports progressive transmission, offers a concise encoding of the original mesh, and permits selective refinement. The paper presents a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. Unlike previous simplification methods, this procedure seeks to preserve not just the geometry of the mesh surface, but more importantly its overall appearance, as defined by discrete and scalar attributes such as material identifiers, color values, normals, and texture coordinates. The PM representation is demonstrated using several practical models. The PM representation is constructed by first simplifying a mesh through a sequence of edge collapse transformations, resulting in a coarser mesh. This coarser mesh is then used to generate a sequence of vertex split transformations that, when applied in reverse, reconstruct the original mesh. The PM representation thus defines a continuous sequence of meshes of increasing accuracy, from which LOD approximations of any desired complexity can be efficiently retrieved. Moreover, geomorphs can be efficiently constructed between any two such meshes. The PM representation also naturally supports progressive transmission, offers a concise encoding of the original mesh, and permits selective refinement. The paper also discusses the advantages of PM over multiresolution analysis (MRA). PM is lossless, while MRA requires that the detail terms lie on a domain with subdivision connectivity, and as a result an arbitrary initial mesh can only be recovered to within an ε tolerance. In contrast, the PM representation is lossless since M^n = M. Additionally, the PM representation can have arbitrary connectivity, allowing for much better approximations than their MRA counterparts. Finally, PM can introduce surface creases anywhere, while MRA cannot effectively deal with surface creases unless they lie parametrically along edges of the base mesh.Progressive meshes (PM) are a new representation for storing and transmitting arbitrary triangle meshes. This paper introduces PM, which provides an efficient, lossless, continuous-resolution representation that addresses several practical problems in computer graphics, including smooth geomorphing of level-of-detail (LOD) approximations, progressive transmission, mesh compression, and selective refinement. The PM representation is constructed by simplifying a mesh through a sequence of edge collapse transformations, followed by a sequence of inverse vertex split transformations. This results in a continuous sequence of meshes of increasing accuracy, from which LOD approximations of any desired complexity can be efficiently retrieved. Moreover, geomorphs can be efficiently constructed between any two such meshes. The PM representation also naturally supports progressive transmission, offers a concise encoding of the original mesh, and permits selective refinement. The paper presents a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. Unlike previous simplification methods, this procedure seeks to preserve not just the geometry of the mesh surface, but more importantly its overall appearance, as defined by discrete and scalar attributes such as material identifiers, color values, normals, and texture coordinates. The PM representation is demonstrated using several practical models. The PM representation is constructed by first simplifying a mesh through a sequence of edge collapse transformations, resulting in a coarser mesh. This coarser mesh is then used to generate a sequence of vertex split transformations that, when applied in reverse, reconstruct the original mesh. The PM representation thus defines a continuous sequence of meshes of increasing accuracy, from which LOD approximations of any desired complexity can be efficiently retrieved. Moreover, geomorphs can be efficiently constructed between any two such meshes. The PM representation also naturally supports progressive transmission, offers a concise encoding of the original mesh, and permits selective refinement. The paper also discusses the advantages of PM over multiresolution analysis (MRA). PM is lossless, while MRA requires that the detail terms lie on a domain with subdivision connectivity, and as a result an arbitrary initial mesh can only be recovered to within an ε tolerance. In contrast, the PM representation is lossless since M^n = M. Additionally, the PM representation can have arbitrary connectivity, allowing for much better approximations than their MRA counterparts. Finally, PM can introduce surface creases anywhere, while MRA cannot effectively deal with surface creases unless they lie parametrically along edges of the base mesh.