Scene Graphs

Definition

A scene graph is a tree structure representing hierarchical relationships between objects in a scene.

Transformation Inheritance

Child objects inherit transformations from parent nodes:

• Each node has its own local transformation
• World transformation = product of all parent transformations

Traversal Pseudocode

traverse(node, T_parent):
    M = T_parent * node.T * node.E
    node.draw(M)
    for child in node.children:
        traverse(child, T_parent * node.T)

where:

• node.T: Transformation relative to parent
• node.E: Optional additional transformation (e.g., animation)

Example: Robot Arm

Body → Shoulder → UpperArm → Elbow → LowerArm → Hand

• Body: Positioned in world space
• Shoulder: Rotates relative to body
• Elbow: Rotates relative to upper arm
• Hand: Rotates relative to lower arm

Each transformation is relative to its parent.

Benefits

• Natural representation of articulated objects
• Easy animation (just modify local transforms)
• Efficient rendering (traverse tree, accumulate transforms)
• Supports instancing (same object under different parent nodes)

Summary

• Scene graphs organise objects hierarchically
• Children inherit parent transformations
• Traversal accumulates transformations down the tree
• Natural for articulated objects and animations

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Past Paper Questions

2021 Paper 3 Question 4: Explain how scene graphs work. How are transformations accumulated?