Презентация - Math end algebra. Vector

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Презентация Math end algebra. Vector


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Math end algebra. Vector, слайд 1
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Math end algebra. Vector, слайд 2
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MATH & ALGEBRA
MATH & ALGEBRA
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VECTOR
VECTOR
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Length Pythagorean Formula |V| = sqrt(x2 + y2)
Length Pythagorean Formula |V| = sqrt(x2 + y2)
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Addition A = (1, 2) B = (4, 0) A + B = (1+4, 2+0) = (5, 2)
Addition A = (1, 2) B = (4, 0) A + B = (1+4, 2+0) = (5, 2)
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Subtraction A = (1, 2) B = (4, 0) A - B = A + (-B) A - B = (1-4, 2-0) = (-3, 2)
Subtraction A = (1, 2) B = (4, 0) A - B = A + (-B) A - B = (1-4, 2-0) = (-3, 2)
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Scalar Multiplication A*3 = (3*1, 3*2) = (3, 6) (unit vector = divide the vector by it's length
Scalar Multiplication A*3 = (3*1, 3*2) = (3, 6) (unit vector = divide the vector by it's length)
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Dot Product
Dot Product
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Cross Product
Cross Product
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Real world examples In which direction should the missile be fired to hit the target? Is the enemy v
Real world examples In which direction should the missile be fired to hit the target? Is the enemy visible in the field of view? How far is the bullet from the window?
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Solutions Solutions have been done by many before. Know the basics to find them quicker. Use utils a
Solutions Solutions have been done by many before. Know the basics to find them quicker. Use utils and classes like: Vector3D Vector3DUtils Plane3D, Ray (4. 0) Vector3
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Math end algebra. Vector, слайд 13
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Spaces Euclidean space using Cartesian coordinates. (X, Y and Z) Local/Model Space World Space View/
Spaces Euclidean space using Cartesian coordinates. (X, Y and Z) Local/Model Space World Space View/Camera Space (Point-of-view) Screen space (2D)
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Left- and right-handed systems
Left- and right-handed systems
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MATRICES AND SPACES
MATRICES AND SPACES
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Matrices Matrix = Transformation placeholder So again: Local/Model matrix World matrix View/Camera m
Matrices Matrix = Transformation placeholder So again: Local/Model matrix World matrix View/Camera matrix WVP = world * view * projection
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Classes/Utils Matrix3D Matrix3DUtils Matrix4x4
Classes/Utils Matrix3D Matrix3DUtils Matrix4x4
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TRANSFORMATIONS
TRANSFORMATIONS
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Linear transformation Translation
Linear transformation Translation
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Linear transformation Scale
Linear transformation Scale
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Linear transformation Skew
Linear transformation Skew
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Linear transformation Eulers Quaternions Avoids gimbal lock Slerp (Smooth interpolated rotation) Mat
Linear transformation Eulers Quaternions Avoids gimbal lock Slerp (Smooth interpolated rotation) Matrix – memory intensive
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Multi linear transformation Stack of matrices Apply all at once to an object The order is importent
Multi linear transformation Stack of matrices Apply all at once to an object The order is importent Identity matrix
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Nonlinear transformations Sin curve displacement Warp
Nonlinear transformations Sin curve displacement Warp
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PROJECTIONS
PROJECTIONS
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Most common projections
Most common projections
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GRAPHICS PIPELINE
GRAPHICS PIPELINE
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Programmable pipeline
Programmable pipeline
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Math end algebra. Vector, слайд 30
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Math end algebra. Vector, слайд 31
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Math end algebra. Vector, слайд 32
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Math end algebra. Vector, слайд 33
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Math end algebra. Vector, слайд 34
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Math end algebra. Vector, слайд 35
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Math end algebra. Vector, слайд 36
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Math end algebra. Vector, слайд 37
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Math end algebra. Vector, слайд 38
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Math end algebra. Vector, слайд 39
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Stages overview
Stages overview
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SHADERS
SHADERS
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About shaders Small programs that runs on the GPU. Most shader languages are the same. Vertex and Fr
About shaders Small programs that runs on the GPU. Most shader languages are the same. Vertex and Fragment shaders work in pairs. The pair is compiled into a Program Uniforms, Attributes, Varyings, Built in attributes
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Low level shading language Assembly language ARB (GPU) AGAL (Adobe Graphics Assembly Language)
Low level shading language Assembly language ARB (GPU) AGAL (Adobe Graphics Assembly Language)
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High level shading languages HLSL – DirectX API Cg – NVIDIA GLSL – OpenGL ShaderLab – Unity3D PixelB
High level shading languages HLSL – DirectX API Cg – NVIDIA GLSL – OpenGL ShaderLab – Unity3D PixelBender3D – Molehill HxSL – haXe Shader
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Vertex shader VS or VSH Executed at each vertex Transform between coordinate systems Lighting Define
Vertex shader VS or VSH Executed at each vertex Transform between coordinate systems Lighting Defines the final position of that vertex Outputs some variables to the Fragment shader.
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Geometry Shader Dynamic creation of geometry on the GPU Only Shader Model 4. 0 Direct3D 10, OpenGL 3
Geometry Shader Dynamic creation of geometry on the GPU Only Shader Model 4. 0 Direct3D 10, OpenGL 3. 2 Not available in OpenGL ES 2. 0 (Molehill, webGL)
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Fragment Shader FSH Processed at each visible fragment Fragment != Pixel Handles bump effects, shado
Fragment Shader FSH Processed at each visible fragment Fragment != Pixel Handles bump effects, shadows and lights, reflections, refractions, textures, ray casting and other effects. Output is a pixel color in the format RGBA
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Texture objects Texels Power of Two (POT) 2, 4,…512, 1024 pixels Flipped pixel order (OpenGL) Intege
Texture objects Texels Power of Two (POT) 2, 4,…512, 1024 pixels Flipped pixel order (OpenGL) Integer/Floating-point
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Texture Filtering Fixing artifacts Texture magnification/minification Mipmapping Different technique
Texture Filtering Fixing artifacts Texture magnification/minification Mipmapping Different techniques:
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Let’s have a look at the WegGL implementation (click on image) three. js
Let’s have a look at the WegGL implementation (click on image) three. js
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Cubemap texture
Cubemap texture
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Shader tool examples Shader Toy – WebGL MeShade – WebGL PixelBender3D – Molehill Node Based Shader E
Shader tool examples Shader Toy – WebGL MeShade – WebGL PixelBender3D – Molehill Node Based Shader Editor – Unity3D
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Interior mapping
Interior mapping
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Animations, Skin and Bones Tweens Animation controllers Blending Mixing/Additive Vertex animations i
Animations, Skin and Bones Tweens Animation controllers Blending Mixing/Additive Vertex animations in shader Procedurally animating
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Animations in Away3D Broomstick
Animations in Away3D Broomstick
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Materials Material is the collection of properties applied to an object. Shaders is the implemention
Materials Material is the collection of properties applied to an object. Shaders is the implemention. ”The code” In Unity, think that materials is a collection of exposed properties of the shader.
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Some ingredients: Color Diffuse: base color Ambient: color of ambient light (shadowed parts). Mostly
Some ingredients: Color Diffuse: base color Ambient: color of ambient light (shadowed parts). Mostly the same as diffuse. Specular: Highlight color Emissive: Glow. Overrides shadows. Alpha: Transparency Texture (2D,Cubemap) Shininess: size of specular highlights (gloss) Reflection/Refraction Bump-mapping: height, grayscaled image Normal-mapping: Dot3 bump mapping, xyz->rgb Paralax-mapping: height + direction, graycaled+rgb
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Example
Example
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Unitys Normal Shader Family
Unitys Normal Shader Family
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Lighting Uses normals Directional/point-lights Material settings to decide final color. Lighting is
Lighting Uses normals Directional/point-lights Material settings to decide final color. Lighting is computed at each vertex. Light mapping (beast) Deferred shading
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Lambert shading
Lambert shading
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Real-time shadows
Real-time shadows
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Quality and performance Non realtime-shadows fastest! Shadow map resolution Number of lights
Quality and performance Non realtime-shadows fastest! Shadow map resolution Number of lights
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Example in Unity
Example in Unity
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Special effects Effects Color correction Postprocessing stage / GPU LDR/HDR, Tone mapping
Special effects Effects Color correction Postprocessing stage / GPU LDR/HDR, Tone mapping
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Math end algebra. Vector, слайд 66
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Physics
Physics
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Very simple physics demo
Very simple physics demo
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Frameworks Goal: Games, experimental, Vizualisation? Reach: Plugin? Multiple platforms/screens? Cost
Frameworks Goal: Games, experimental, Vizualisation? Reach: Plugin? Multiple platforms/screens? Cost: Open source? Licenced? Support: Large community?
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Math end algebra. Vector, слайд 70
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Unity3D Boo, C# and JavaScript Plugin Great and simple IDE Competent and mature framework Pro versio
Unity3D Boo, C# and JavaScript Plugin Great and simple IDE Competent and mature framework Pro version to get all goodies Multiple screens/targets Future: Export to flash/molehill
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Math end algebra. Vector, слайд 72
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Flash/Molehill Actionscript Plugin 3D content always under the DisplayList All the other stuff in th
Flash/Molehill Actionscript Plugin 3D content always under the DisplayList All the other stuff in the flash player. Molehill currently in alpha
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Flash 3D Engines
Flash 3D Engines
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Optimizing Profiling memory usage, cleanup/destroy Object Pooling! polygonal lab Take control of ren
Optimizing Profiling memory usage, cleanup/destroy Object Pooling! polygonal lab Take control of rendering pipeline Compression/Model to ByteArray AWD, Away3Ds own format (Prefab) Trends of resource-load in online 3D? Optimize opcodes in swf:
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Math end algebra. Vector, слайд 76
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WebGL Javascript No plugin Open / Royalty-free Not available in all browsers yet Frameworks in early
WebGL Javascript No plugin Open / Royalty-free Not available in all browsers yet Frameworks in early states Probably available on iOS soon
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WebGL Frameworks
WebGL Frameworks
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Jellyfish
Jellyfish
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Particles
Particles
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Hello Racer
Hello Racer
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Clouds
Clouds
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WebGL vs. Molehill APIs HTML5 vs. Plugin. WebGL will probably run in iOS browser. Easy to port betwe
WebGL vs. Molehill APIs HTML5 vs. Plugin. WebGL will probably run in iOS browser. Easy to port between them. Once it running on the GPU, performance is hardware related regardless of API. It is the high level frameworks that makes the difference.
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Debugging Profiling CPU FlashPreloadProfiler Profiling GPU Pix for windows Intel® Graphics Performan
Debugging Profiling CPU FlashPreloadProfiler Profiling GPU Pix for windows Intel® Graphics Performance Analyzers (GPA)
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3D Model filetypes
3D Model filetypes
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Learning tips
Learning tips
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Random interesting topics
Random interesting topics
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Random interesting topics Level of detail
Random interesting topics Level of detail
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Random interesting topics Octree, BSP Tree, Portals and Sectors
Random interesting topics Octree, BSP Tree, Portals and Sectors
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Random interesting topics Global illumination / Ambient occlusion
Random interesting topics Global illumination / Ambient occlusion
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Random interesting topics Raytracing/Raycasting/Raymarching
Random interesting topics Raytracing/Raycasting/Raymarching
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Some useful resources
Some useful resources
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Books and papers Away3D 3. 6 essentials Mathematics for Game Developer by Christopher Tremblay Mathe
Books and papers Away3D 3. 6 essentials Mathematics for Game Developer by Christopher Tremblay Mathematics for 3D Game Programming and Computer Graphics by Eric Lengyel Game Graphics Programming by Allen Sherrod Realtime shadows Raycasting in GPU shaders by Joost van Dongen
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Thanks! Wow! You made it all the way here! I hope you got inspired to continue your journey into the
Thanks! Wow! You made it all the way here! I hope you got inspired to continue your journey into the third dimension. Thanks for listening! twitter. com/inear


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