8.5.4 Edge setup quadratic case8.5.4.1 Mathematical backgroundIt is also possible to setup the limiters to incrementally calculate the followingequation:fdycxbyaxyxf ++++= 22),(At the origin the value is like this:ff =)0,0(The step in x direction is like this:12)(),1()(12),(12)1()1(),1(2222++=−+=+++=+++++++=++++++=+caxxfyxfxdxcaxyxffdyccxbyaxaxfdyxcbyxayxfThe step in y direction is like this:12)(),1()(12),(12)1()1()1,(2222++=−+=++=+++++++=++++++=+dbyxfyxfydybxyxffddycxbybyaxfydcxybaxyxfIn the quadratic case the increments dx , dy depend on x and y and are notconstant. They can be calculated incrementally:acaxcxaxdxxdxxd 2)12(1)1(2)()1(2 =++−+++=−+=bdbydybydyydyyd 2)12(1)1(2)()1(2 =++−+++=−+=At the Origin the increments are like this:1)0( += cdx and 1)0( += ddyWith incrementing the value by dx , dy for every step in x and y direction andincrementing dx , dy by xd 2 , yd 2 for every step in x and y direction the quadraticequation can be easily calculated for the whole bounding box.Drawing Engine Chapter 8Preliminary User's Manual S19203EE1V3UM00 231
