Fast Forward to Practical Assignment Drawing a Line 76
Drawing a Line 77
Drawing a Line 78
Drawing a Line Some things to consider Which pixels are to be drawn? How thick the lines are? How to join lines? 79
Drawing a Line 80
Drawing a Line We need some basic math: 81
Drawing a Line We need some basic math: x=x1 y=y1 while(x<x2) plot(x,y) x++ y+=Dy 82
Drawing a Line After rounding 83
Drawing a Line Great, but what about accumulated error? 84
Drawing a Line What about steep lines? |m| ≤ 𝟐 |m| > 𝟐 85
Drawing a Line First code void drawLine(int x1, int x2, int y1, int y2) { float m = (y2-y1)/(x2-x1); int x = x1; float y = y1; while(x<=x2) { setPixel(x, round(y), PIXEL_ON); x += 1; y += m; } } 86
Drawing a Line It has some issues void drawLine(int x1, int x2, int y1, int y2) { float m = (y2-y1)/(x2-x1); not exact! int x = x1; float y = y1; while(x<=x2) { setPixel(x, round(y), PIXEL_ON); x += 1; y += m; accumulates error! } } 87
Drawing a Line First changes, use error threshold void drawLine(int x1, int x2, int y1, int y2) { float m = (y2-y1)/(x2-x1); int x = x1; int y = y1; float e = 0.0f; while(x<=x2) { setPixel(x, round(y), PIXEL_ON); x += 1; e += m; if(e>0.5f) { y += 1; e -= 1.0f; } } } 88
Drawing a Line More changes, error condition to 0 void drawLine(int x1, int x2, int y1, int y2) { int x = x1; int y = y1; float e = -0.5f; while(x<=x2) { setPixel(x, round(y), PIXEL_ON); x += 1; e += (y2-y1)/(x2-x1); if(e>0.0f) { y += 1; e -= 1.0f; } } } 89
Drawing a Line More changes, splitting up the fraction void drawLine(int x1, int x2, int y1, int y2) { int x = x1; int y = y1; float e = -0.5f*(x2-x1); while(x<=x2) { setPixel(x, y, PIXEL_ON); x += 1; e += y2-y1; if(e>0.0f) { y += 1; e -= x2-x1; } } } 90
Drawing a Line More changes, get rid of floats void drawLine(int x1, int x2, int y1, int y2) { int x = x1; int y = y1; int e = -(x2-x1); while(x<=x2) { setPixel(x, y, PIXEL_ON); x += 1; e += 2*(y2-y1); if(e>0) { y += 1; e -= 2*(x2-x1); } } } 91
Drawing a Line Jack E. Bresenham, 1962 Fast, no floating points, only for |𝑛| < 1 and 𝑦1 < 𝑦2 void drawLine(int x1, int x2, int y1, int y2) { int x = x1; int y = y1; int e = -(x2-x1); while(x<=x2) { setPixel(x, y, PIXEL_ON); x += 1; e += 2*(y2-y1); if(e>0) { y += 1; e -= 2*(x2-x1); } } } 92
PPGSO Project OpenGL Project (simple demo / scene / game ) 93
OpenGL Project - No engines allowed (NO Unity, Unreal engine etc.) - You can cooperate, help each other - Libraries for resource loading are allowed - Evaluated is graphical output, interaction and animation - Gameplay is secondary (is not scope of this lecture) 94
OpenGL Project Specification [6p] Data structures (1p) Class diagrams (1p) Pseudocodes (1p) User interaction diagrams (1p) Structure rendering algorithms (1p) Modul connection diagrams (1p) Use of texture mapping on 3D geometry [4p] Unique 3D meshes (2p) Unique texturing using uv coordinates (2p) Camera transformations [6p] Camera with perspective projection (1p) Animated camera (2p) Interactive camera (2p) Use of multiple camera view positions (1p) 95
OpenGL Project Scene logic [5p] Implementation of a scene with logically relative objects (1p) Changing scenes and multiple areas/scenes (2p) At least 2 different scenes Scene has a logical ground and background (sky, ceiling, walls…) (1p) Presented demo must have a beginning and a logical ending (1p) Objects and interactions [6b] Dynamic scene with objects being created and destroyed during demo simulation (1p) At least 2 different types of objects Procedurally generated scene (2b) Constraints and deterministic definitions for object localization Effective object to object collisions and interactions (3p) Dynamic response to collisions 96
OpenGL Project Transformations and animation [9b] Procedurally driven animation (2p) Encapsulated method with parameters Logical branching Basic simulated animation with at least 2 forces using matrix algebra (2p) Eg. gravity + wind Hierarchical object transformation (2p) At least 2 levels with 3 objects Using the aggregation and transformation matrices Data driven animations, recommended using key-frames (3p) Key-frame sequence represented by code structure of transformation matrix and time information Interpolation using curves or quaternions and spherical linear interpolation 97
OpenGL Project Lighting with multiple light sources [7b] Diffuse scene lighting with materials (2p) Changeable color of light (1b) Correct Phong lighting with multiple light sources (2p) Correct depth-based attenuation At least 3 material and light components Correctly combine material and light components Correct shadows or reflections using any approach you can think of (2p) Project report (pdf) [7b] 1xA4 description of the project manual + runnable package (1b) 2xA4 screens from the projects + game video (2b) Critical evaluation and update of the specification (4b) 98
OpenGL Project Get a project! https://tinyurl.com/y3jdfms4 Subject information: https://tinyurl.com/y6244wyn 99
Next Week 2D Transformations 3D Transformations Projections 100
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