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These are the Lecture Slides of Advanced Data Structures which includes Split Algorithm, Unbalanced Binary Search Trees, Forward Pass, Forward Pass Example, Backward Cleanup Pass, Retrace Path, Current Nodes, Roots of Respective Tries, Branch Nodes etc. Key important points are: Bsp Trees, Binary Space Partitioning Trees, Collection of Objects, Dimensional Hyperplanes, Classifying Object, Intersection Points, Coincident List, Dimensional Space, Collision Detection
Typology: Slides
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n-dimensional space
splitting hyperplane (n-1)-dimensional a 1 x 1 + a 2 x 2 + … anxn + an+1 = 0 ax + by + c = 0 (2D) ax+by+cz+d = 0 (3D)
n-dimensional space +ve half space ax + by + c > 0 ax+by+cz+d > 0
-ve half space ax + by + c < 0 ax+by+cz+d < 0
coincident ax + by + c = 0 ax+by+cz+d = 0
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Equation of ph is z – 2 = 0 General: ax + by + cz + d = 0
n-dimensional space
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if O is empty , return null ; Create a new node N ; N.ph = partitioning hyperplane for O ; lList = rList = N.cList = null ; for each object z in O do if z is coincident to ph or |O| = 1, add z to N. cList ; if z is left of ph , add z to lList ; if z is right of ph , add z to rList ; if z spans ph , split z and add pieces to lList and rList ; N.leftChild = BSPTree(lList); N.rightChild = BSPTree(rList); return N;
{ draw(N.rightChild); draw N.cList; draw(N.leftChild) };
{ draw(N.leftChild); draw N.cList; draw(N.rightChild) };
{ draw(N.leftChild); draw N.cList; draw(N.rightChild) };
{ draw(N.rightChild); draw N.cList; draw(N.leftChild) };
