1. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Lab 9: 3D & Projections Basics

2. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Tutorial contents Introduction to Projections Basic Concepts Projection Types and Matrix Orthographic Solve 2 Exam Qestions

3. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Introduction to Projections We live in a 3D world but the screen where the rendered objects appear is a 2D space. Thus, we need to convert somehow our 3D world to 2D. The operation which does this conversion is called projection. When Programming we focus on 2 main types of projections Orthographic – casts parallel rays of light from the scene to projection plane Perspective – casts angled rays of light from the scene to projection plane Perspective projection generates a realistic effect since our vision works the same way

4. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Basic Concepts camera coordinate system viewport coordinate system device/screen coordinate system

5. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Projection Type - Orthographic r 0 – a vector pointing from world origin to Projection plane origin r – object point vector (from world origin to P) P – object point P’ – projected point U – view direction Z’ – distance from P to P’ along U r’ – P’ coordinates in word CS u 1,u 2 – projected image main axis x’,y’ – P’ coordinate in image CS P P’

6. Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering Projection Matrix - Orthographic When U is Orthogonal to u 1 and u 2 we can simplify the equations to get the matrix If U is not orthogonal (like in oblique parallel) we must use the equations given in the lecture

7. Solve 2 Midterm questions Solve 2 midterm questions Technion - Israel Institute of Technology Faculty of Mechanical Engineering Laboratory for CAD & Lifecycle Engineering