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Title: 3D Viewing and Orthogonal Projections 13D Viewing and Orthogonal Projections Chapter 5 and 7.6.2 in Hill 2IntroductionIn this week and next week, we will discuss how viewing and perspective transformations are handled for 3-D spaces. In particular, we will look at how OpenGL performs drawing of 3D scenes. In OpenGL and most similar graphics systems, the process involves three basic steps 1. Modelview transformation 2. Perspective transformation 3. Mapping to the viewport 33-D coordinate systemBasically, we will assume that all of the objects defined are initially represented relative to a standard 3-dimensional coordinate frame called world coordinate that follow a right-hand coordinate system.yxz 4Basic steps in 3D DrawingModelview transformation Maps objects (actually vertices) from their world-coordinate representation to one that is centered around the viewer. The resulting coordinates are called eye-coordinates Perspective projection This projects points in 3-D eye-coordinates to points on a plane called viewplane. This projection process consists of two separate parts the projection transformation (affine) and clipping. Mapping to the viewport Convert the point from these 2-D coordinate to the viewport (pixel) coordinates. 52D Drawing (so far)2D drawing is based on a special case of 3D viewing. a) parallel projection b) the eye or camera is along the z-axis at the window or viewplane, a rectangle lying on in the xy-plane c) the view volume is the parallelepiped 62D Drawing (cont.)Points lying in the view volume will are projected onto the window along lines parallel to z-axis Points lying outsides the view volume will be clipped off Function provided by OpenGL is glOrtho2D(left, right, bottom, top) 73D DrawingIn 3-D drawing, the camera or eye will have more flexibility in term of position and orientation to produce better views of the scene. Example below shows the position and orientation of a camera or eye in a scene.In this scene, the block has undergone transformation process from its original shape which is a cube and displayed using parallel projection. 83D Drawing (cont.)Basically, this is done by OpenGL where it provides functions to define the view volume and its position. We will look at the details of drawing 3D scene using parallel projection. 9OpenGL Graphics PipelineAgain we will look at the OpenGL graphics pipeline Each vertex will have to go through this pipeline. They will encounter three matrices before being displayed on the screen. 10Modelview MatrixModelview matrix This matrix combines two effects the sequence of modeling transformation applied to

Page 1 of 4Use the video and step-by-step drawing instructions below to learn how to draw Monkey D. Luffy from the Manga and Anime One Piece. A new cartoon drawing tutorial is uploaded every week, so stay tooned!Intro: Start off with a pencil sketch. In the beginning stages, don’t press down too hard. Use light, smooth strokes for sketching.Step 1: Start by drawing a big circle in the middle of the page. This will be the basic shape for the top part of Monkey D. Luffy's head. The circle doesn’t have to be perfect. It’s just a guide.Step 2: Draw a curved line under the circle as a guide for Monkey D. Luffy's chin and jaw. The line should have a small point near the middle for the chin. Together these two shapes form the guide for the head.Step 3: Next, draw two intersecting lines across the entire head, one vertical and one horizontal. Bend the lines so that they contour to the shape. These will be construction lines that will help you place Monkey D. Luffy's facial features later on.Step 4: Draw two small circles as guides for Monkey D. Luffy's eyes. Draw them sitting on top of the horizontal construction line and on either side of the vertical construction line. The circle on the right should be a bit smaller because of perspective.Step 5: On the left side of Monkey D. Luffy's head, draw a curved line similar to a backward letter C as a guide for the ear. The top of the C-shaped line should be placed at the end of the horizontal construction line on the left.

Light travelling from the object to the user's eye and to the drawing surface, where the rays intersect with the drawing surface, that's our projection of the object.Simple.There is concept in the illustration above worth noting, as we'll be using it in the following discussion.That is the distance between the drawing surface and the view point; it's referred to as d by the CSS Transforms Module Level 2 spec.Here's what d is in the illustration above:d - the distance between the view point and the drawing surface (or the z=0 plane)As we shall learn later on in this chapter, the perspective() function and the perspective property are both used to specify this distance.Demonstrating perspective using 3D objectsEven though we demonstrated perspective here using a 2D object, we could do so using a 3D object as well. But that would obviously require a more intricate illustration and also a whole virtual 3D space modeled to be able to visualize the effect of perspective in that illustration clearly.So far the sake of brevity, we have omitted including such an example. The concept is nonetheless still the same.And to add to this fact, individual elements on webpages are all 2D objects; likewise, this argument becomes even more practical.The perspective() functionThe perspective() transform function is used to establish perspective in the projection of an object on the screen.perspective() specifies the distance between the view point and the z=0 plane, which is merely the drawing surface.It essentiall specifies the d that we showcased in the illustration above.The larger the distance, the more elaborate the projection. Similarly, the smaller the distance, the more subtle the projection. (Remember this.)Here's the syntax of the perspective() function:perspective( | none)It can either have a value in the range 0 to ∞ (infinity), for e.g. 30px, or the keyword value none.Let's