Rendering equation

In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced into computer graphics by David Immel et al.^[1] and James Kajiya^[2] in 1986. The various realistic rendering techniques in computer graphics attempt to solve this equation.

The physical basis for the rendering equation is the law of conservation of energy. Assuming that L denotes radiance, we have that at each particular position and direction, the outgoing light (L_o) is the sum of the emitted light (L_e) and the reflected light (L_r). The reflected light itself is the sum from all directions of the incoming light (L_i) multiplied by the surface reflection and cosine of the incident angle.

^ Immel, David S.; Cohen, Michael F.; Greenberg, Donald P. (1986). "A radiosity method for non-diffuse environments" (PDF). In David C. Evans; RussellJ. Athay (eds.). SIGGRAPH '86. Proceedings of the 13th annual conference on Computer graphics and interactive techniques. pp. 133–142. doi:10.1145/15922.15901. ISBN 978-0-89791-196-2. S2CID 7384510.
^ Kajiya, James T. (1986). "The rendering equation" (PDF). In David C. Evans; RussellJ. Athay (eds.). SIGGRAPH '86. Proceedings of the 13th annual conference on Computer graphics and interactive techniques. pp. 143–150. doi:10.1145/15922.15902. ISBN 978-0-89791-196-2. S2CID 9226468.

[1] Immel, David S.; Cohen, Michael F.; Greenberg, Donald P. (1986). "A radiosity method for non-diffuse environments" (PDF). In David C. Evans; RussellJ. Athay (eds.). SIGGRAPH '86. Proceedings of the 13th annual conference on Computer graphics and interactive techniques. pp. 133–142. doi:10.1145/15922.15901. ISBN 978-0-89791-196-2. S2CID 7384510.

[2] Kajiya, James T. (1986). "The rendering equation" (PDF). In David C. Evans; RussellJ. Athay (eds.). SIGGRAPH '86. Proceedings of the 13th annual conference on Computer graphics and interactive techniques. pp. 143–150. doi:10.1145/15922.15902. ISBN 978-0-89791-196-2. S2CID 9226468.

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