COMP2004-CGAssignment 131stAugust, 2020COMP2004 Computer GraphicsAssignment 1, 2020@ Computing Discipline, Curtin UniversityWeighting:This assignment contains 13 questions, for a total of 100 points,which weights for 20% of the final mark.Submission:You only need to submita single PDFfile containing neatlytyped answers.No photos or scansare accepted. You canuse drawing feature on your word processor. Name the file as__Assignment01.pdf. Use a cover page thatincludes necessary information, such as your name, student ID.This assignment is due on 28 September 2020, 9 AM (UTC+8)Academic Integrity:This is anindividualassignment so that any form of collabo-ration is not permitted. This is anopen-bookassignment sothat you are allowed to use external materials, but make sureyou properly paraphrase and cite the references. It is your re-sponsibility to understand Curtin’s Academic Misconduct Rules,for example, posting assessment questions online and asking foranswers is considered as contract cheating and not permitted.General Computer Graphics Concepts1. (5 points) Provide the detailed justification on why we need to use theHomogenous form matrices for transformation (Refer to lecture 2 and 3).Why is it not a good idea to have an additional vector instead? Providean example in your justification.2. (5 points) In 3D graphics rendering pipeline, describe the purpose ofVertex ProcessorandFragment Processor.3. (5 points) Why GPU (Graphics Processing Unit) is essential nowadaysfor Computer-Graphics-related tasks? Why not using only CPU (CentralProcessing Unit)? Justify your answer.4. (5 points) Draw the diagram and describe every step of the ViewingPipeline.Computer Graphics - Assignment 1Page 2 of 631stAugust, 2020Geometrical Transformations5. (10 points) Find 2D transformation matrices to transform cyan object toorange object in Figure 1. Please provide textual explanation on whatyou are trying to do with those matrices step by step. You do NOT haveto multiply them into a single final matrix.Figure 1: Find transformation matrices to transform cyan object to orange object.6. (10 points) Find 3D row representation transformation matrices to per-form:scaling on reference pointP13,7,−2>with triple on x and zcoordinates, but halved on y coordinate, followed byreflection onX=Yplane, followed byreflection on a straight line that passes through pointP22,3,4>andP35,6,4>Please provide textual description to justify your answer.Computer Graphics - Assignment 1Page 3 of 631stAugust, 2020Projection Transformations7. (6 points) Describe how you calculate x* and z* step-by-step for Case 2single-point perspective transformation where the COP (Center or Pro-jection) is located at the origin, and the projection plane is located atY=Yp0. Your calculation should show the final projection matrix aswell.8. (7 points) Imagine you have a unit cube centered at0,0,0.5>. Cal-culate and draw its projected image on YZ plane with DOP1,2,0>.(Parallel Projection)9. (7 points) Imagine you have a solid 2D square with side length 2 centeredat coordinate0,0,−3>and normal vector1,0,0>. Calculate anddraw its projected image on Z=0 plane with the COP0,0,−10>.(Perspective Projection)Computer Graphics - Assignment 1Page 4 of 631stAugust, 2020Graphical Objects Representation10. (10 points) Have a look at the partial 2D circle at Figure 2. Find theimplicitandparametricrepresentation of it on 2D space (ignore Z).Figure 2: Partial circle on XY plane. Find the parametric and implicit representation.11. (10 points) You have learned on how to create 2D solid circle in para-metric representation. Please do some research to find out how to createa 3D hollow cone (only the surface, and the base is not solid). Show theparametric representation on which the base of the cone is located at theorigin with radius 1, aligned with XZ plane, and the peak is located at0,5,0>. Provide explanation along with your equation.Figure 3: Hollow Cone.Computer Graphics - Assignment 1Page 5 of 631stAugust, 2020Non-Programming QuestionsThe following questions are open-ended questions. There is no unique an-swer, but it has to be logical, detailed, and contain mathematical expla-nations. These questions might help you get better intuition on the futureOpenGL assignment. However, you doNOTneed to use programming-related informations (e.g functions names or parameters) to answer them.12. (10 points) Imagine that you have a human-shaped object located atlocation Hh, Yh, Zh>and a camera located at Cc, Yc, Zc>.Imagine this is a video game with the camera act as a main character ina first-person view. You can move and rotate the camera anywhere in realtime, but not flying above or below the eye level. How do you proposeto have the human-shaped object always facing the camera all the time,so that you always see only the front side of the object? (Assume thereis no other objects obstructing the view)Note: If you only answer ”I will have the object always faces the camera”,you will get zero marks due to insufficient explanation. You need math-ematical explanation as well. Keep asking yourself how you can achievethe task. For example: ”how do I face the camera?”, ”how do I know theangle?”, ”How often do I need to update the position and orientation?”,”What should happen if the camera is not facing the object?”13. (10 points) Imagine that you have a planar surface acting as a wall with4 corners located atW10,0,0>, W20,1,0>, W31,1,0>, W41,0,0>. Once again, imagine that the camera as a main character youcontrol with a first-person view. The main character is holding a dartarrow with invisible hand in front of the camera. How do you proposeto keep the dart in front of the camera all the time when the camera ismoving? It means that the dart is always facing the correct orientation(pointy end away from the camera)? How will you do the transformationto throw the dart in a straight line infinitely? (how to determine thedirection?) What can you do to make the dart stop flying when it hit thewall? (Let dart location asD d, Yd, Zd>)Computer Graphics - Assignment 1Page 6 of 631stAugust, 2020