Results 1  10
of
31
Defining pointset surfaces
 ACM Trans. Graph. (Proceedings of ACM SIGGRAPH
, 2004
"... The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. ..."
Abstract

Cited by 138 (2 self)
 Add to MetaCart
The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. This definition reveals connections to research in computer vision and computational topology. Variants of the MLS surface can be created by varying the vector field and the energy function. As an example, we define a similar surface determined by a cloud of surfels (points equipped with normals), rather than points. We also observe that some procedures described in the literature to take points in space onto the MLS surface fail to do so, and we describe a simple iterative procedure which does. the relationship of extremal surfaces and implicit surfaces. As we discuss in Section 5, there is an implicit surface containing every extremal surface, including the MLS surface. This can be quite useful, particularly for defining normals precisely. 1
Approximating and Intersecting Surfaces from Points
, 2003
"... Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each poin ..."
Abstract

Cited by 67 (3 self)
 Add to MetaCart
Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted covariances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zeroset is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted covariances are well defined in a tubular neighborhood of the surface. For certain, wellchosen weight functions we can show that wellsampled surfaces lead to smooth distance fields with nonzero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute raysurface intersections for fast ray casting and ray tracing of the surface.
Algebraic point set surfaces
 In Proceedings SIGGRAPH ’07
, 2007
"... Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Samp ..."
Abstract

Cited by 42 (4 self)
 Add to MetaCart
Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Sample positions are partly highlighted. In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.
A Barcode Shape Descriptor for Curve Point Cloud Data
, 2004
"... In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD). Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. We also provide a metric over the space ..."
Abstract

Cited by 24 (15 self)
 Add to MetaCart
In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD). Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. We also provide a metric over the space of barcodes, enabling fast comparison of PCDs for shape recognition and clustering. To demonstrate the feasibility of our approach, we implement our pipeline and provide experimental evidence in shape classification and parametrization.
Approximating Bounded, Nonorientable Surfaces from Points
 In Shape Modeling International
, 2004
"... We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally nonorientable surfaces. The surface is defined implicitly using directions of weighted covariances and weighted averages of the points. Specifically, a point belongs ..."
Abstract

Cited by 23 (3 self)
 Add to MetaCart
We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally nonorientable surfaces. The surface is defined implicitly using directions of weighted covariances and weighted averages of the points. Specifically, a point belongs to the surface, if its direction to the weighted average has no component into the direction of smallest covariance. For bounded surfaces, we require in addition that any point on the surface is close to the weighted average of the input points. We compare this definition to alternatives and discuss the details and parameter choices. Points on the surface can be determined by intersection computations. We show that the computation is local and, therefore, no globally consistent orientation of normals is needed. Continuity of the surfaces is not affected by the particular choice of local orientation. We demonstrate our approach by rendering several bounded (and nonorientable) surfaces using ray casting.
Integral Invariants for Robust Geometry Processing
 IN: ICCV ’95: PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON COMPUTER VISION. IEEE COMPUTER SOCIETY
, 2005
"... ..."
Efficient raytracing of deforming pointsampled surfaces
 Computer Graphics Forum
, 2005
"... We present efficient data structures and caching schemes to accelerate raysurface intersections for deforming pointsampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compar ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
We present efficient data structures and caching schemes to accelerate raysurface intersections for deforming pointsampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compared to existing techniques. Starting from a tight bounding sphere hierarchy for the undeformed object, we use a lazy updating scheme to adapt the hierarchy to the deformed surface in each animation step. In addition, we achieve a significant speedup for raysurface intersections by caching perray intersection points. We also present a technique for rendering sharp edges and corners in pointsampled models by introducing a novel surface clipping algorithm.
Hardware rendering of 3D geometry with elevation maps
 In Proc. International Conference on Shape Modeling and Applications
, 2006
"... We present a generic framework for realtime rendering of 3D surfaces. We use the common elevation map primitive, by which a given surface is decomposed into a set of patches. Each patch is parameterized as an elevation map over a planar domain and resampled on a regular grid. While current hardware ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We present a generic framework for realtime rendering of 3D surfaces. We use the common elevation map primitive, by which a given surface is decomposed into a set of patches. Each patch is parameterized as an elevation map over a planar domain and resampled on a regular grid. While current hardware accelerated rendering approaches require conversion of this representation back into a triangle mesh or point set, we propose to render the elevation maps directly in a hardware accelerated environment. We use one base data set to render each patch in the common vertex and fragment shader pipeline. We implement meshor pointbased rendering by using a base mesh or a base point set respectively. This provides the basis for the underlying primitive for the final rendering. We show the benefits of this method for splat rendering by replacing attribute blending through a simplified and fast attribute interpolation. This results in rendering acceleration as well as an improvement in visual quality when compared to previous approaches. primitive does not rely on connectivity information and is therefore suitable for applications, such as dynamic shape modelling [25]. Also with regard to efficient rendering, points have shown to be a suitable primitive in hardware accelerated environments [27, 5]. However, current splatting implementations on graphics hardware require several rendering passes for blending attributes of overlapping splats. The blending itself tends to produce blurring artifacts that are visible at a closeup range. We consider hardwarebased rendering of 3D geometry using the heightfield representation [23]. As denoted in figure 1, a given surface is decomposed into a number of patches, each of which is resampled as an elevation map over a compactly supported planar domain, and hence it can be held as a 2D texture. In [23] it has been shown that this representation can be used for highperformance com1
Radiosity for pointsampled geometry
 In Proc. 12th Pacific Conference on Computer Graphics and Applications
, 2004
"... In this paper, we propose a radiosity method for the pointsampled geometry to compute diffuse interreflection of light. Most traditional radiosity methods subdivide the surfaces of objects into small elements such as quadrilaterals. However, the pointsampled geometry includes no explicit informati ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
In this paper, we propose a radiosity method for the pointsampled geometry to compute diffuse interreflection of light. Most traditional radiosity methods subdivide the surfaces of objects into small elements such as quadrilaterals. However, the pointsampled geometry includes no explicit information about surfaces, presenting a difficulty in applying the traditional approach to the pointsampled geometry. The proposed method addresses this problem by computing the interreflection without reconstructing any surfaces. The method realizes lighting simulations without losing the advantages of the pointsampled geometry. 1.
Representing and Rendering Surfaces with Points
, 2003
"... This report deals with the use of points as surface rendering and modeling primitives. The main components of pointbased rendering and modeling algorithms are identified, different approaches are discussed and compared. The weaknesses of current pointbased techniques are pointed out and for some o ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This report deals with the use of points as surface rendering and modeling primitives. The main components of pointbased rendering and modeling algorithms are identified, different approaches are discussed and compared. The weaknesses of current pointbased techniques are pointed out and for some of them a possible solution is suggested. A new algorithm for depthoffield rendering based on surface splatting is presented. It features rendering time independent of the amount of depthblur and depthoffield rendering in scenes with semitransparent surfaces. For this algorithm a mathematical analysis, an implementation and a discussion of results are given.