Abstract: An apparatus and a computer program product render a multi-dimensional digital image using raytracing in a multi-dimensional space. A multi-dimensional digital differential analyzer (DDA) is included. Variables of said multi-dimensional digital differential analyzer (DDA) are set up using multiplications only. The digital image is rendered based upon the variables of the multi-dimensional digital differential analyzer (DDA). Each axis of the multi-dimensional space includes a numerator which holds the progress within a cell along that axis and a denominator which describes a size condition causing said DDA to step to a next cell.

Abstract: An apparatus and a computer program product render a multi-dimensional digital image using raytracing in a multi-dimensional space. A multi-dimensional digital differential analyzer (DDA) is included. Variables of said multi-dimensional digital differential analyzer (DDA) are set up using multiplications only. The digital image is rendered based upon the variables of the multi-dimensional digital differential analyzer (DDA). Each axis of the multi-dimensional space includes a numerator which holds the progress within a cell along that axis and a denominator which describes a size condition causing said DDA to step to a next cell.

Abstract: A method, an apparatus, and a computer program product render a multi-dimensional digital image using raytracing in a multi-dimensional space. Variables of a multi-dimensional digital differential analyzer (DDA) are set up using multiplications only. For each axis of the multi-dimensional space, a numerator holds the progress within a cell along that axis and a denominator describes a size condition causing the DDA to step to a next cell. For a vector, a denominator of the vector for an axis is equal to a delta for a vector component, excluding the component of said axis, for two dimensions; and a product of deltas for all vector components, excluding the component of said axis, for greater than two dimensions.

Abstract: Bounding voxelization of a triangle or other polygon represented in a three-dimensional space is determined by dividing the triangle or polygon into polygons, each being an intersected slice of a grid. Each polygon is rasterized individually to determine an intersection of each edge with voxels on the defined slice for a given axis position. Strips of the voxels are marked iteratively using minimum and maximum voxel positions along a secondary axis for a tertiary axis.

Abstract: A method, an apparatus, and a computer program product are disclosed for rendering a digital image using raytracing in a three-dimensional space. A 3-D digital differential analyzer (DDA) denominator vector describes a size condition for stepping to a next cell. Variables of the denominator vector are setup for a first sample of a first horizontal line of samples. A ray is cast into the 3-D space for a current sample dependent upon the denominator vector. An updated value of the denominator vector for next sample is generated. First and second order differentials for the sample in the horizontal line of samples are incrementally computed using only additions. In this manner, a ray is cast for each sample in the line of samples. Another updated value for the denominator vector for next line of samples is generated. First and second order differentials for the vertical axis are incrementally computed using only additions. In this manner, every line of samples is processed.

Abstract: Bounding voxelization of a triangle or other polygon represented in a three-dimensional space is determined by dividing the triangle or polygon into polygons, each being an intersected slice of a grid. Each polygon is rasterized individually to determine an intersection of each edge with voxels on the defined slice for a given axis position. Strips of the voxels are marked iteratively using minimum and maximum voxel positions along a secondary axis for a tertiary axis.

Abstract: A method, an apparatus, and a computer program product are disclosed for rendering a digital image using raytracing in a three-dimensional space. A 3-D digital differential analyzer (DDA) denominator vector describes a size condition for stepping to a next cell. Variables of the denominator vector are setup for a first sample of a first horizontal line of samples. A ray is cast into the 3-D space for a current sample dependent upon the denominator vector. An updated value of the denominator vector for next sample is generated. First and second order differentials for the sample in the horizontal line of samples are incrementally computed using only additions. In this manner, a ray is cast for each sample in the line of samples. Another updated value for the denominator vector for next line of samples is generated. First and second order differentials for the vertical axis are incrementally computed using only additions. In this manner, every line of samples is processed.

Abstract: A method, an apparatus, and a computer program product render a multi-dimensional digital image using raytracing in a multi-dimensional space. Variables of a multi-dimensional digital differential analyzer (DDA) are set up using multiplications only. For each axis of the multi-dimensional space, a numerator holds the progress within a cell along that axis and a denominator describes a size condition causing the DDA to step to a next cell. For a vector, a denominator of the vector for an axis is equal to a delta for a vector component, excluding the component of said axis, for two dimensions; and a product of deltas for all vector components, excluding the component of said axis, for greater than two dimensions.