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Exam Template COM3503 COM3503 1 TURN OVER Data Provided: None DEPARTMENT OF COMPUTER SCIENCE Autumn Semester 2020-2021 3D COMPUTER GRAPHICS 2 Hours Answer THREE questions only. All questions carry equal weight. Figures in square brackets indicate the percentage of available marks allocated to each part of a question. COM3503 COM3503 2 This page is blank COM3503 COM3503 3 1. Figure 1 shows a quadcopter model made entirely from spheres, where each sphere is transformed into the required shape for the particular part. The central body of the quadcopter has four arms attached to it. Within each arm, at the end of the horizontal piece, the darker-coloured piece contains an engine to rotate the rotor blade assembly attached above it. A rotor blade assembly consists of a sphere and two rotor blades, each of which is tilted slightly in its direction of travel. a) The transformations required to create the relationships between the pieces is the focus of this part of the question, rather than the actual size of the pieces. (i) Draw a scene graph for the model. Include transformation nodes. Assume that a method exists to draw a sphere with its origin at its centre – this will affect the transformations used. Where branches or subbranches are similar, use a brief statement describing this rather than drawing the whole branch. [35%] (ii) State where you would place transformations in your scene graph to control a vertical ascent (take-off). As the quadcopter ascends, the rotor blades should rotate around their respective vertical axes. In your answer, briefly discuss any need to link different transformation nodes in the scene graph. [15%] (iii) Discuss the transformation(s) necessary to control the length of one of the arms of the quadcopter. The engine and rotor blade assembly should not change size and should remain positioned at the end of the arm. In your answer, state where the transformation(s) would be positioned in the scene graph and briefly discuss how this would affect the different parts of the hierarchy. [15%] b) Assume the quadcopter is modelled using a polygon mesh model. One of the triangles in the mesh is composed of the vertices p0 = (2, 0, 0), p1 = (0, 2, 0), and p2 = (0, 0, 2), listed in anticlockwise order. The camera is at the world coordinate position (4, 5, 6) looking at the world origin. Using relevant vectors and calculations, determine whether or not the triangle should be back face culled. Full working out must be shown. Note: The cross product for vectors a = (ax, ay, az) and b = (bx, by, bz) is given by a × b = (aybz−azby, azbx−axbz, axby−aybx). [20%] c) Consider that one of the quadcopter’s engines is on fire and producing a lot of smoke. A solution based on particle systems and billboards is proposed. A free- roaming camera is being used to view the scene. Outline three possible visual problems when rendering the smoke effect in conjunction with the quadcopter model. [15%] Figure 1. A quadcopter toy. The grid of lines is the xz plane. COM3503 COM3503 4 2. This question makes use of Figures 2 and 3 (on the next page), which show a vertex and a fragment shader, respectively. Consider that these shaders are used in the rendering of a polygon mesh object. Line numbers are included in Figures 2 and 3 to make it easy to refer to particular lines of code in this question and in your answers. a) Describe two visual effects that result from setting the calculation in line 29 of the fragment shader to a value of 0. [10%] b) State both changes required to the fragment shader code if the light source was a directional light source, i.e. effectively positioned at infinity. [10%] c) Describe the purpose of line 15 in the vertex shader. [10%] d) The vertex and fragment shaders implement a particular local reflection model. Describe two omissions in the model, i.e. factors that occur in reality that the model does not deal with. [10%] e) Consider a fragment with aPos=(0,0,7) and aNormal=(0,0,1). The light (fragment shader lines 10-17) has position=(12,0,23), ambient=(0.3,0.3,0.3), diffuse=(1,1,1) and specular=(1,1,1). The material (fragment shader lines 19-26) has ambient=(0,0.5,0), diffuse=(0,0.8,0), specular=(0,0,0), shininess=1. Thus the fragment has no specular component. Calculate the diffuse intensity for the fragment. You must show your full working out in your answer. [20%] f) Consider the fragment in 2(e). The material’s specular value is changed to (1,1,1), with a shininess value of 128. Where would a viewer have to be positioned to see a specular highlight on the fragment and what direction should they be looking in? [10%] g) A simple hidden surface removal method that deals with complete polygons is called the Painter’s algorithm. A polygon list is built up in memory that contains for each polygon a single depth value (for example the depth of the centroid). Polygons are then rendered into screen memory in order of depth, the furthest polygon being dealt with first. Compare and contrast the z-buffer approach to hidden surface removal with the Painter’s algorithm, using the following criteria: (i) Memory required and scene complexity; [15%] (ii) Depth correctness of final rendering. Consider both static and animated scenes in your answer. [15%] COM3503 COM3503 5 Figure 2. A vertex shader 01: #version 330 core 02: 03: layout (location = 0) in vec3 position; 04: layout (location = 1) in vec3 normal; 05: 06: out vec3 aPos; 07: out vec3 aNormal; 08: 09: uniform mat4 model; 10: uniform mat4 mvpMatrix; 11: 12: void main() { 13: gl_Position = mvpMatrix * vec4(position, 1.0); 14: aPos = vec3(model*vec4(position, 1.0f)); 15: aNormal = mat3(transpose(inverse(model))) * normal; 16: } 01: #version 330 core 02: 03: in vec3 aPos; 04: in vec3 aNormal; 05: 06: out vec4 fragColor; 07: 08: uniform vec3 viewPos; 09: 10: struct Light { 11: vec3 position; 12: vec3 ambient; 13: vec3 diffuse; 14: vec3 specular; 15: }; 16: 17: uniform Light light; 18: 19: struct Material { 20: vec3 ambient; 21: vec3 diffuse; 22: vec3 specular; 23: float shininess; 24: }; 25: 26: uniform Material material; 27: 28: void main() { 29: vec3 ambient = light.ambient * material.ambient; 30: 31: vec3 norm = normalize(aNormal); 32: vec3 lightDir = normalize(light.position - aPos); 33: float diff = max(dot(norm, lightDir), 0.0); 34: vec3 diffuse = light.diffuse * diff * material.diffuse; 35: 36: vec3 viewDir = normalize(viewPos - aPos); 37: vec3 reflectDir = reflect(-lightDir, norm); 38: float spec = pow(max(dot(viewDir, reflectDir), 0.0), 39: material.shininess); 40: vec3 specular = light.specular * spec * material.specular; 41: 42: vec3 result = ambient + diffuse + specular; 43: fragColor = vec4(result, 1.0); 44: } Figure 3. A fragment shader (split into two pieces to fit everything on one page) COM3503 COM3503 6 3. a) Two common approaches used to produce shadows in polygon mesh rendering are shadow maps (i.e. the shadow z-buffer approach) and shadow volumes. Briefly contrast the two approaches with respect to each of the following statements, making sure you include comments on each approach in each of your answers: (i) The approach allows objects to cast shadows on themselves (i.e. self- shadowing); [10%] (ii) The approach renders the scene geometry from the viewpoint of the light; [10%] (iii) The approach generates extra geometric primitives; [10%] (iv) The resolution of the intermediate representation used in the approach can result in problems with aliasing. [10%] b) An animation sequence is required for a very old alien’s face represented as a polygon mesh model. The skin of the face is green and also has blotches of different colours. Some of these blotches are yellow and some are a metallic, shiny colour that reflect objects in the