In 3D computer graphics, the Phong reflection model is an illumination and shading model for assigning shades to points on a modeled surface. It was developed by Bui Tuong Phong in his University of Utah Ph.D. dissertation "Illumination for Computer Generated Pictures" in 1973, in conjunction with a method for interpolating the calculation for each individual pixel that is rasterized from a polygonal surface model; the interpolation technique is known as Phong shading, even when it is used with a reflection model other than Phong's. This article or section does not adequately cite its references or sources. ... Bui Tuong Phong (Vietnamese: Bùi Tường Phong, 1942–1975) was a Vietnamese-born computer graphics researcher and pioneer. ... The University of Utah (also The U or the U of U or the UU) is a public university in Salt Lake City, Utah. ... D.Sc. ... This example shows an image with a portion greatly enlarged, in which the individual pixels are rendered as little squares and can easily be seen. ... It has been suggested that Phong reflection model be merged into this article or section. ...

The Phong reflection model can be treated as a simplification of the more general rendering equation; it takes advantage of the following simplifications when deciding the shade of a point on a surface: In computer graphics, the rendering equation describes the flow of light energy throughout a scene. ...

1. It is a local reflection model, i.e. it doesn't account for second-order reflections, as do ray tracing and radiosity. In order to compensate for the loss of some reflected light, an extra ambient lighting term is added to the scene that is rendered.
2. It divides the reflection from a surface into three subcomponents, specular reflection, diffuse reflection, and ambient reflection.

If we first define, for each light source in the scene to be rendered, the components i_s and i_d, where these are the intensities (often as RGB values) of the specular and diffuse components of the light sources respectively. A single i_a term controls the ambient lighting; it is sometimes computed as a sum of contributions from the light sources. A ray traced scene. ... Radiosity is a global illumination algorithm used in 3D computer graphics rendering. ... The RGB color model utilizes the additive model in which red, green, and blue light are combined in various ways to create other colors. ...

If we then define, for each material (which is typically assigned 1-to-1 for the object surfaces in the scene):

k_s: specular reflection constant, the ratio of reflection of the specular term of incoming light

k_d: diffuse reflection constant, the ratio of reflection of the diffuse term of incoming light (Lambertian reflectance)

k_a: ambient reflection constant, the ratio of reflection of the ambient term present in all points in the scene rendered

α: is a shininess constant for this material, which decides how "evenly" light is reflected from a shiny spot

We further define lights as the set of all light sources, L is the direction vector from the point on the surface toward each light source, N is the normal at this point of the surface, R is the direction a perfectly reflected ray of light (represented as a vector) would take from this point of the surface, and V is the direction towards the viewer (such as a virtual camera). If a surface exhibits Lambertian reflectance, light falling on it is scattered such that the amount of light an observer sees, the surface luminance, is the same regardless of their angle of view. ... In mathematics, a set can be thought of as any collection of distinct things considered as a whole. ... A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...

Then the shade value for each surface point I_p is calculated using this equation, which is the Phong reflection model:

The diffuse term does not use the direction towards the viewer (V), as the diffuse term is equal in all directions from the point, including the direction of the viewer. The specular term, however, is large only when the reflection vector R is nearly aligned with viewpoint vector V, as measured by the α power of the cosine of the angle between them, which is the dot product of the normalized direction vectors R and V. When α is large, representing an almost mirror-like reflection, the specular reflection will be very small because the high power of the cosine will go rapidly to zero with any viewpoint not aligned with the reflection. In mathematics, the dot product, also known as the scalar product, is a binary operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. ...

When we have color representations as RGB values, this equation will typically be calculated individually for R, G and B intensities.

Phong reflection is an empirical model, which is not based on a physical description of light interaction, but instead on informal observation. Phong observed that for very shiny surfaces the specular highlight was small and the intensity fell off rapidly, while for duller surfaces it was larger and fell off more slowly. Bui Tuong Phong (Vietnamese: Bùi Tường Phong, 1942–1975) was a Vietnamese-born computer graphics researcher and pioneer. ...

This equation can be represented in a graphic way: Image File history File links Size of this preview: 800 × 223 pixel Image in higher resolution (963 × 268 pixel, file size: 47 KB, MIME type: image/png) Illustration of the Phong Reflection Model. ...

Here the "ambient" and "diffuse" colors are the same; note that the intensity of the diffuse component varies with the direction of the surface whereas the ambient component is uniform. The "specular" color is white, reflecting almost all of the light hitting the surface, but only in very narrow highlights.

Phong shading interpolation method

Main article: Phong shading

Along with the reflection model for computing color at a surface point, Bui Tuong Phong also developed a method of interpolation to compute colors at every pixel in a rasterized triangle representing a surface patch. These topics are sometimes treated together under the term Phong shading, but here the latter term is used only for the interpolation method. It has been suggested that Phong reflection model be merged into this article or section. ... Bui Tuong Phong (Vietnamese: Bùi Tường Phong, 1942–1975) was a Vietnamese-born computer graphics researcher and pioneer. ... It has been suggested that Phong reflection model be merged into this article or section. ...

See also

• Bui Tuong Phong : Read about this shading model creator's life and work.
• Specular highlight
• Blinn-Phong reflection model : A later alteration of Phong's model
• Bidirectional reflectance distribution function : Another reflection model