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  1. Implementing Scene Graphs,CSG Trees Glenn G. U. of Alaska Fairbanks CS 481/681 Lecture Notes Monday, January 26, 2004

  2. Review:Data Structures for Scenes • We will discuss four types of trees for holding scenes: • Scene Graphs • Organized by how the scene is constructed. • Nodes hold objects. • CSG Trees • Organized by how the scene is constructed. • Leaves hold 3-D primitives. Internal nodes hold set operations. • BSP Trees • Organized by spatial relationships in the scene. • Nodes hold facets (in 3-D, polygons). • Quadtrees & Octrees • Organized spatially. • Nodes represent regions in space. Leaves hold objects. CS 481/681

  3. Review:The Basics of Scene Graphs [1/2] • Structure of a (simple) scene graph: • Each node corresponds to a drawable object. • The children of a given node correspond to “parts” of the object; these may be movable. • Thus, each node has a transformation. It, and all of its descendants, are drawn with this transformation. • The descendants have, in addition, their own transformations. • Data needed in each node: • Drawable object (pointer to this?). • Transformation (a matrix? a pointer to a matrix? a pointer to a function that returns a matrix?). • Pointers to child nodes. CS 481/681

  4. Review:The Basics of Scene Graphs [2/2] • In face.cpp, if we stored the face in a scene graph, it might look like this: • We can add functionality to scene graphs by putting other things in them. In particular: • Light sources. • Other things like light sources (e.g., environment maps). Head Hair Eye Eye Ear Ear Nose Mouth Iris Iris L. R. Pupil Pupil CS 481/681

  5. Implementing Scene Graphs:Overview • Now we look at how to implement a scene graph. • What type of tree to use. • The node data structure. • Drawing via a simple recursive traversal. • Deallocation issues. • Lastly, we look briefly at a “DAG” variation, in which we do not use a tree. CS 481/681

  6. Implementing Scene Graphs:Using B-Trees • We often implement an arbitrary tree as a binary tree. • We distinguish between the logical tree and the physical tree. The latter is the internal representation, which may be entirely hidden. • Each node has a “down” pointer to its first (logical) child and a “right” pointer to the next (logical) child of its (logical) parent. • Either or both of these may be null. • A pre-order traversal of the physical tree gives a reasonable (pre-order, roughly speaking) traversal of the logical tree. Logical Tree Physical Tree CS 481/681

  7. Implementing Scene Graphs:Node Implementation • Say a node is an object of class SGNode. Each node needs: • An object:(Drawable *). • A transformation. • I will use an array of 16 GLdouble’s. You may want to do this differently. • Down pointer & right pointer: (SGNode *). class SGNode { public: // Lots of stuff here: constructor(s), etc. void drawtree() const; // Draw objects in my subtree. private: Drawable * object; // Must be valid. GLdouble transform[16]; // Handle differently?? SGNode * downp; // Each of downp, rightp is SGNode * rightp; // either valid or null. }; CS 481/681

  8. Implementing Scene Graphs:Drawing Via Tree Traversal • Now writing drawtree is easy: recursively traverse the tree. • Stuff hanging off of downp uses this node’s transformation, but stuff hanging off of rightp does not. void SGNode::drawtree() const { glPushMatrix(); glMultMatrixd(transform); // Handle differently?? object->draw(); // virtual function call if (downp) downp->drawtree(); glPopMatrix(); if (rightp) rightp->drawtree(); } • Draw the scene by calling drawtree for the root node. CS 481/681

  9. Implementing Scene Graphs:The Node Destructor • Everything needs to be deallocated. Generally, in a tree, each node is responsible for freeing its children. SGNode::~SGNode() { // Is the node responsible for delete'ing its object? // If not, then you don't want the line below. delete object; // transform is just an array member; we can ignore // it here. But if your transformation uses dynamic // allocation, you should probably deallocate it now. if (downp) delete downp; if (rightp) delete rightp; } CS 481/681

  10. Implementing Scene Graphs:DAG Variation • A Directed Acyclic Graph (DAG) is a generalization of a tree. • Different nodes can share children. • Thus, a node may not have a unique parent. • We do not allow “cycles”: a node cannot be its own descendant. • The 2-child-pointer idea does not work for a DAG. (Why not?) • DAG’s are particularly appropriate for scene graphs, since identical objects can appear more than once in a scene. • This means that an object cannot store its own transformation. Instead, it stores the transformations of its children. • Deallocation gets interesting; a parent no longer “owns” its children. • Solution 1: Each node keeps a reference count. When it hits 0, deallocate. • Solution 2: Nodes do not manage each other at all. Keep all nodes in a list. CS 481/681

  11. CSG Trees:Introduction to CSG • We have constructed scenes with polygons (and points & lines). • Another method is Constructive Solid Geometry (CSG). • In CSG, primitives are solid 3-D objects. For example, • Sphere • Cube • Cylinder • Cone • Etc. … • We create new objects from existing ones using three set operations: • Union • Intersection • Set difference • CSG does not work well with pipeline-based rendering, so we will say little about it right now. • CSG scenes are typically rendered using some type of ray tracing. • The movie Tron (Disney, 1982) used CSG-style techniques. • CSG is less mainstream than it used to be. • I am told it is still used in CAD. CS 481/681

  12. CSG Trees:Scene Representation • In CSG, we represent a scene as a binary tree. • Leaves hold primitives. • Internal nodes, which always have two children, hold set operations. • The order in which children are given matters (for the set-difference operation). • CSG trees are useful for things other than rendering. • Intersection tests (collision detection, etc.) are not too hard. (Thus: ray tracing.) • A DAG may be appropriate here as well. U U U ∩ – sphere sphere cube cone sphere cube CS 481/681

  13. A Brief Introduction to BSP Trees • A very different way of storing a scene is a Binary Space Partition tree (BSP tree). • BSP trees are useful for visibility-related issues, HSR, etc. • Nodes hold polygons. • In 3-D nodes hold polygons. In 2-D they would hold line segments. • Thus, a BSP tree provides a relatively low-level description of a scene. • Data about the arrangement of the scene is encoded in the structure of the tree. • Details on the board … CS 481/681