Digital differential analyzer (graphics algorithm): Difference between revisions

Revision as of 07:13, 14 February 2019

Revision as of 07:21, 11 April 2019

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In [[computer graphics]], a '''digital differential analyzer''' ('''DDA''') is hardware or software used for [[interpolation]] of [[Variable (computer science)|variables]] over an [[Interval (mathematics)|interval]] between start and end point. DDAs are used for [[rasterization]] of lines, triangles and polygons. They can be extended to non linear functions, such as [[texture mapping#Perspective correctness|perspective correct texture mapping]], [[quadratic curves]], and traversing [[voxels]].

In its simplest implementation for linear cases such as [[Line (geometry)|line]]s, the DDA algorithm interpolates values in interval by computing for each x_i the equations x_i = x_i−1 + 1, y_i = y_i−1 + m, where Δxm =is x_endthe −[[slope]] x_startof andthe line. Δy =This y_endslope −can y_startbe andexpressed min DDA =as Δy/Δxfollows:

:<math>m = \frac{y_{\rm end} -y_{\rm start}}{x_{\rm end}-x_{\rm start}}</math>

== Performance ==

where ''m'' represents the slope of the line and ''c'' is the y intercept. In fact any two consecutive pointpoints (x,y) lying on this line segment should satisfy the equation.

== Performance ==

The DDA method can be implemented using [[floating-point]] or [[integer]] arithmetic. The native floating-point implementation requires one addition and one rounding operation per interpolated value (e.g. coordinate x, y, depth, color component etc.) and output result. This process is only efficient when an [[Floating-point unit|FPU]] with fast add and rounding operation will be available.

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DDAs are well suited for hardware implementation and can be pipelined for maximized throughput.

This slope can be expressed in DDA

as

:<math>m = \frac{y_{\rm end} -y_{\rm start}}{x_{\rm end}-x_{\rm start}}</math>

where ''m'' represents the slope of the line and ''c'' is the y intercept. In fact any two consecutive point(x,y) lying on this line segment should satisfy the equation.

== Algorithm ==