Bilinear texture mapping—more precisely, bilinear texture filtering—estimates a color between texture samples by blending the four nearest texels. Each texel’s contribution depends on how far the sampling point lies from it, so the result changes smoothly across the texture.
What bilinear texture filtering does
A texture is a grid of discrete color samples called texels. A rendered surface, however, can be sampled at a position between those texels: its UV coordinates do not have to land exactly on a texel center. The sampler uses bilinear filtering to estimate the color at that in-between position.
It takes the four texels surrounding the sample and calculates a weighted average. Microsoft Learn describes this as calculating “the weighted average of the 4 texels closest to the sampling point” (Microsoft Learn: Texture filtering).
How the four texels are blended
Imagine four neighboring texels at the corners of a square: C00 and C10 along one side, and C01 and C11 along the other. Let u and v be the sample’s fractional horizontal and vertical offsets within that square, each between 0 and 1. The interpolated color is:
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C(u,v) = (1−u)(1−v)C00 + u(1−v)C10 + (1−u)vC01 + uvC11
The four weights sum to 1. A texel contributes most when the sample is near it, and its contribution falls as the sample moves toward the opposite corner. At a texel’s own sample position, it contributes fully and the other three contribute nothing. Exactly at the shared corner between four texels, each contributes one quarter. In Microsoft’s example with red, green, blue, and white texels, that equal blend produces gray, RGB (128, 128, 128) (Microsoft Learn: Texture filtering).
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Why it is called bilinear
The calculation is equivalent to performing two linear interpolations in succession: first between texels along one texture axis, then between those intermediate values along the other. This is the tensor-product form of linear interpolation in two dimensions (University of Texas at Austin: Texture Mapping; University of Illinois Urbana-Champaign: Textures). Some graphics systems label the axes or order the texels differently; the essential point is that the two fractional offsets determine the four weights.
Why graphics use it
A texture sampler must return a color for each rendered sample even when the mapped coordinate falls between texels. Nearest-point sampling simply chooses one texel, which can make enlarged textures look blocky. Bilinear filtering averages nearby values and usually makes magnified textures appear smoother (Microsoft Learn: Texture filtering).
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That smoothing is not the same as recovering detail that the texture does not contain. Bilinear filtering can still look chunky or leave jagged edges, and it does not by itself address all the problems that arise when a texture is reduced or viewed at an angle.
Bilinear, trilinear, mipmapping, and anisotropic filtering
These terms describe related but different parts of texture sampling. Bilinear filtering blends texels within one 2D texture level; other techniques address changes in scale or the shape of the visible texture footprint.
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| Technique | What it does | Useful distinction |
|---|---|---|
| Nearest-point sampling | Selects one nearby texel. | Does not blend the surrounding colors; may look blocky. |
| Bilinear filtering | Blends four nearby texels on a single texture level. | Smooths sampling within that level, but does not alone solve minification or oblique-view issues. |
| Mipmapping | Provides progressively lower-resolution versions of a texture. | Helps when a texture is minified; using mipmaps requires additional texture memory. |
| Trilinear filtering | Combines bilinear samples from two mipmap levels, interpolating between levels. | Adds interpolation along the mip-level dimension; it is not just another name for bilinear filtering. |
| Anisotropic filtering | Improves sampling when the projected texture footprint is stretched or angled relative to the view. | Can preserve detail in cases where simple mipmap or bilinear filtering looks blurred. |
Microsoft characterizes linear filtering’s added computational cost as usually negligible on modern graphics hardware, while noting its visual limitations. Mipmaps and anisotropic filtering address different image-quality trade-offs (Microsoft Learn: Texture filtering; Microsoft Learn: Mipmaps).
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Coordinates and texture edges
The sampler interprets the texture coordinates in the texture grid’s coordinate system, identifies the neighboring samples, and uses the fractional parts of the coordinates for interpolation. What happens when a coordinate falls outside the nominal 0–1 range depends on the configured addressing behavior. For example, course notes from the University of Illinois show wrapping an out-of-range coordinate back into that interval before converting it to grid coordinates (University of Illinois Urbana-Champaign: Textures).
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Coordinate orientation is also a convention, not a universal rule. Microsoft’s UWP documentation uses (0,0) at the top-left and (1,1) at the bottom-right, with texels centered in grid cells; other APIs and image pipelines can define orientation or address handling differently (Microsoft Learn: Texture filtering).
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