Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7CSC 480 / 580Computer GraphicsK. KirbyScene Graphsand Slerping QuaternionsNKU CSC 480 KIRBYclass Widget{public: void dump() const ; virtual void spin(); virtual void toss() =0 ; void flip() { toss() ; } // ... } ;Remembering OOWidgetFastWidgetSlowWidgetSlowWidget sw ;FastWidget fw ;play( sw ) ;play( fw ) ;void play( Widget* p ){ p->toss() ; // ...} void play( Widget* p ){ p->toss() ; // ...} class SlowWidget : public Widget{public: void toss() { /*...*/ } ; void spin() { /*...*/ } ; // ...} ;class FastWidget : public Widget{public: void toss() { /*...*/ } ;// ...} ;NKU CSC 480 KIRBYsphere: GlutSpherecenter: TransformNode west: TransformNode east: TransformNode east: TransformNoderedMat: MaterialNodegreenMat: MaterialNode blueMat: MaterialNodelight: LightNodelight2: LightNodescene: NodeA simple scene graph instanceThis is a DAG(directed acyclic graph)NKU CSC 480 KIRBYNodeNodeTransformNodeTransformNodeEnvironmentNodeEnvironmentNodeAppearanceNodeAppearanceNodeLightNodeLightNodeMaterialNodeMaterialNodeArtifactNodeArtifactNodeMeshMeshGlutSphereGlutSphereGlutTeapotGlutTeapotA Simple Scene Graph Class HierarchyNKU CSC 480 KIRBYImplementation Issues for DiscussionHow do we implement a DAG ?What does a TransformNode do?How to we handle rendering of sub-scenes?How do clients assemble a scene graph in an OpenGL program?NKU CSC 480 KIRBYSee SceneGraph.h, SceneGraph.cpp, DemoSceneGraph.cppR(0)R(1)Frame 442 Frame 482Frame 462 R(0.5) = 0.5 R(0) + 0.5 R(1) ????Bad. Why?Rotation matrices and TweeningNKU CSC 480 KIRBYPoints – as pure quaternionsp = xi + yj + zk Rotations (u^,  ) – as unit quaternionsr = cos ½ + (sin ½) u1i + u2j + u3k Implementing rotations: p´ = r p r* SLERPing quaternions (“spherical linear interpolation”)r(t) = [ sin(1-t) r(0) + sin t  r(1) ] / sin  where cos  = r(0) r(1).NKU CSC 480