Hidden surface determination

In 3D computer graphics, hidden surface determination (also known as hidden surface removal (HSR), occlusion culling (OC) or visible surface determination (VSD)) is the process used to determine which surfaces and parts of surfaces are not visible from a certain viewpoint. A hidden surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics. The process of hidden surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. The analogue for line rendering is hidden line removal. Hidden surface determination is necessary to render an image correctly, so that one cannot look through walls in virtual reality.


Hidden surface determination is a process by which surfaces which should not be visible to the user (for example, because they lie behind opaque objects such as walls) are prevented from being rendered. Despite advances in hardware capability there is still a need for advanced rendering algorithms. The responsibility of a rendering engine is to allow for large world spaces and as the world’s size approaches infinity the engine should not slow down but remain at constant speed. Optimising this process relies on being able to ensure the deployment of as few resources as possible towards the rendering of surfaces that will not end up being rendered to the user.

There are many techniques for hidden surface determination. They are fundamentally an exercise in sorting, and usually vary in the order in which the sort is performed and how the problem is subdivided. Sorting large quantities of graphics primitives is usually done by divide and conquer.


Considering the rendering pipeline, the projection, the clipping, and the rasterization steps are handled differently by the following algorithms:

Culling and visible surface determination

A related area to visible surface determination (VSD) is culling, which usually happens before VSD in a rendering pipeline. Primitives or batches of primitives can be rejected in their entirety, which usually reduces the load on a well-designed system.

The advantage of culling early on the pipeline is that entire objects that are invisible do not have to be fetched, transformed, rasterized or shaded. Here are some types of culling algorithms:

Viewing frustum culling

The viewing frustum is a geometric representation of the volume visible to the virtual camera. Naturally, objects outside this volume will not be visible in the final image, so they are discarded. Often, objects lie on the boundary of the viewing frustum. These objects are cut into pieces along this boundary in a process called clipping, and the pieces that lie outside the frustum are discarded as there is no place to draw them.

Backface culling

Main article: Back-face culling

With 3D objects, only half of the surfaces are facing the camera, and the rest are facing away from the camera, i.e. are on the back side of the object, hindered by the front side. If the object is completely opaque, those surfaces never need to be drawn. They are determined by the vertex winding order: if the triangle drawn has its vertices in clockwise order on the projection plane when facing the camera, they switch into counter-clockwise order when the surface turns away from the camera.

Incidentally, this also makes the objects completely transparent when the viewpoint camera is located inside them, because then all the surfaces of the object are facing away from the camera and are culled by the renderer. To prevent this the object must be set as double-sided (i.e. no backface culling is done) or have separate inside surfaces.

Contribution culling

Often, objects are so far away that they do not contribute significantly to the final image. These objects are thrown away if their screen projection is too small. See Clipping plane.

Occlusion culling

Objects that are entirely behind other opaque objects may be culled. This is a very popular mechanism to speed up the rendering of large scenes that have a moderate to high depth complexity. There are several types of occlusion culling approaches:

Hansong Zhang's dissertation "Effective Occlusion Culling for the Interactive Display of Arbitrary Models"[1] describes an occlusion culling approach.

Divide and conquer

A popular theme in the VSD literature is divide and conquer. The Warnock algorithm pioneered dividing the screen. Beam tracing is a ray-tracing approach which divides the visible volumes into beams. Various screen-space subdivision approaches reducing the number of primitives considered per region, e.g. tiling, or screen-space BSP clipping. Tiling may be used as a preprocess to other techniques. ZBuffer hardware may typically include a coarse 'hi-Z' against which primitives can be rejected early without rasterization, this is a form of occlusion culling.

Bounding volume hierarchies (BVHs) are often used to subdivide the scene's space (examples are the BSP tree, the octree and the kd-tree). This allows visibility determination to be performed hierarchically: effectively, if a node in the tree is considered to be invisible then all of its child nodes are also invisible, and no further processing is necessary (they can all be rejected by the renderer). If a node is considered visible, then each of its children need to be evaluated. This traversal is effectively a tree walk where invisibility/occlusion or reaching a leaf node determines whether to stop or whether to recurse respectively.

See also


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