A game involves a contest between dinosaurs and giant robots. The animation of a robot is simulated using a hierarchical scene graph, whereas a dinosaur is modelled using a skinned animation skeleton. a) A robot is humanoid, consisting of a body, a head, two upper arms, two lower arms, two hands, two upper legs and two lower legs. Explain, step-by step, how the position of a tool in a robot's hand is calculated in world space, using a hierarchical scene graph. [12 marks] b) A dinosaur is modelled as a skinned mesh on an animated skeleton of nodes. The position of the dinosaur's upper and lower arm nodes are calculated in the same manner as a scene graph. Explain the additional calculation, and required data, to compute the position of a vertex on the skinned model near the dinosaur's elbow (i.e. it is influenced by both upper and lower arm nodes). [10 marks] c) The game is set in a large world so there is often the requirement to draw multiple dinosaurs and robots in the distance. Briefly identify two methods which may improve either the performance or appearance of such a scene, clearly stating why the improvement is achieved. [8 marks]