Volumenrepräsentation

Volumenrepräsentation refers to methods used in computer graphics and scientific visualization to represent three-dimensional objects or spaces. Unlike surface-based representations which focus on the boundaries of an object, volumetric representations describe the object or space as a collection of discrete elements, often called voxels (volume elements). These voxels are typically arranged in a regular grid and each voxel stores information about the material, density, color, or other properties at that specific point in space.

One common type of volume representation is the voxel grid. This approach discretizes the 3D space into a uniform grid of cubes. The resolution of the grid, meaning the size of each voxel, directly impacts the level of detail that can be represented. Higher resolution grids offer more detail but require more memory and computational resources. Applications include medical imaging (CT scans, MRI), scientific simulations, and 3D printing data.

Another approach is the octree representation. An octree is a tree data structure in which each internal node has exactly eight children. This structure recursively subdivides a 3D space into eight octants. It is particularly useful for representing sparse or irregularly distributed volumetric data, as it can allocate more detail to regions of interest and less to empty or uniform areas, leading to more efficient storage and processing.

Rendering volumetric data often involves techniques like ray casting or splatting. Ray casting traces rays through the volume, accumulating color and opacity along the ray to determine the final pixel color. Splatting, on the other hand, projects individual voxels onto the image plane, often with a defined shape and blending function.