Abstract: A method produces an image from a set of discrete sample points. The sample points can define a 3D volume or surface. Each discrete sample point is projected to a screen space. A continuous resampling filter for each sample point is generated in screen space. The continuous resampling filter is a combination of a continuous reconstruction function and a continuous filter function for the sample point in screen space. The continuous resampling filter is then applied to each corresponding discrete sample in the screen space to generate a continuous sample for the image. The continuous samples can be rasterized to pixels using any known rasterization process or method.

Abstract: A method of fairing a non-manifold model as disclosed which includes smoothing the model by applying a fairing operator to a set of features such that noise is removed after determining the features of the model.

Abstract: In a method for projecting surface points of a graphic object onto pixels in a depth buffer to determine depth values of the pixels, each surface point is projected onto a corresponding pixels. A depth value of each projected surface point is stored in the pixel only if the depth value of the projected surface point is less than the depth value of the pixel. A tangential disk is constructed at a position of the surface point, the tangential disk has a radius larger than a maximum distance between the surface points. The tangential disk is projected onto a corresponding subset of the pixels. Depth values of the projected tangential disk are stored in the corresponding subsets of pixels only if the depth values of the projected tangential disk are less than the depth values of the corresponding subsets of pixels.

Abstract: A rendering system pipeline includes a memory storing shape and shade attributes of a surface of the object. The attributes are arranged as an octree in the memory. The octree includes a plurality of nodes arranged at a plurality of levels, each node storing a plurality of zero-dimensional n-tuples, each n-tuple locally approximating the shape and shade attributes of a portion of the surface of the graphic object, and the n-tuples having a sampling resolution of an image space. A plurality of parallel processing pipelines are connected the memory. The pipelines project the shape and shade attributes of the octree to an image plane having a selected orientation by traversing the n-tuples of the nodes of the octree from a lowest resolution level to a highest resolution level.

Abstract: In a method for representing a graphic object, rays are cast through the object. The rays originate at orthogonal planes surrounding the object. The surface of the object is sampled for shape and shade attributes at points where the rays intersect the surface. The sampled shape and shade attributes of each sampled point are stored in an octree stored in the memory.

Abstract: A method produces an image from a set of discrete sample points. The sample points can define a 3D volume or surface. Each discrete sample point is projected to a screen space. A continuous resampling filter for each sample point is generated in screen space. The continuous resampling filter is a combination of a continuous reconstruction function and a continuous filter function for the sample point in screen space. The continuous resampling filter is then applied to each corresponding discrete sample in the screen space to generate a continuous sample for the image. The continuous samples can be rasterized to pixels using any known rasterization process or method.

Abstract: In a method for filtering shade attributes of surface points of a graphic object onto pixels in an image buffer according to depth values stored in a depth buffer, tangential disks are constructed at positions of each surface point. The tangential disks have increasingly larger radii. Each tangential disk is projected to an ellipse in texture space. View independent filter functions are applied at the position of each surface point to generate texture mipmaps for the surface point. The filter functions have an extent equal to the projected tangential disk. The surface point is projected to the pixels in the depth buffer, and a view dependent filter function is applied to each pixel in the image buffer to determine colors for the pixels.

Abstract: A method of fairing a non-manifold model as disclosed which includes smoothing the model by applying a fairing operator to a set of features such that noise is removed after determining the features of the model.