🗊Презентация Math end algebra. Vector

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Math end algebra. Vector, слайд №1Math end algebra. Vector, слайд №2Math end algebra. Vector, слайд №3Math end algebra. Vector, слайд №4Math end algebra. Vector, слайд №5Math end algebra. Vector, слайд №6Math end algebra. Vector, слайд №7Math end algebra. Vector, слайд №8Math end algebra. Vector, слайд №9Math end algebra. Vector, слайд №10Math end algebra. Vector, слайд №11Math end algebra. Vector, слайд №12Math end algebra. Vector, слайд №13Math end algebra. Vector, слайд №14Math end algebra. Vector, слайд №15Math end algebra. Vector, слайд №16Math end algebra. Vector, слайд №17Math end algebra. Vector, слайд №18Math end algebra. Vector, слайд №19Math end algebra. Vector, слайд №20Math end algebra. Vector, слайд №21Math end algebra. Vector, слайд №22Math end algebra. Vector, слайд №23Math end algebra. Vector, слайд №24Math end algebra. Vector, слайд №25Math end algebra. Vector, слайд №26Math end algebra. Vector, слайд №27Math end algebra. Vector, слайд №28Math end algebra. Vector, слайд №29Math end algebra. Vector, слайд №30Math end algebra. Vector, слайд №31Math end algebra. Vector, слайд №32Math end algebra. Vector, слайд №33Math end algebra. Vector, слайд №34Math end algebra. Vector, слайд №35Math end algebra. Vector, слайд №36Math end algebra. Vector, слайд №37Math end algebra. Vector, слайд №38Math end algebra. Vector, слайд №39Math end algebra. Vector, слайд №40Math end algebra. Vector, слайд №41Math end algebra. Vector, слайд №42Math end algebra. Vector, слайд №43Math end algebra. Vector, слайд №44Math end algebra. Vector, слайд №45Math end algebra. Vector, слайд №46Math end algebra. Vector, слайд №47Math end algebra. Vector, слайд №48Math end algebra. Vector, слайд №49Math end algebra. Vector, слайд №50Math end algebra. Vector, слайд №51Math end algebra. Vector, слайд №52Math end algebra. Vector, слайд №53Math end algebra. Vector, слайд №54Math end algebra. Vector, слайд №55Math end algebra. Vector, слайд №56Math end algebra. Vector, слайд №57Math end algebra. Vector, слайд №58Math end algebra. Vector, слайд №59Math end algebra. Vector, слайд №60Math end algebra. Vector, слайд №61Math end algebra. Vector, слайд №62Math end algebra. Vector, слайд №63Math end algebra. Vector, слайд №64Math end algebra. Vector, слайд №65Math end algebra. Vector, слайд №66Math end algebra. Vector, слайд №67Math end algebra. Vector, слайд №68Math end algebra. Vector, слайд №69Math end algebra. Vector, слайд №70Math end algebra. Vector, слайд №71Math end algebra. Vector, слайд №72Math end algebra. Vector, слайд №73Math end algebra. Vector, слайд №74Math end algebra. Vector, слайд №75Math end algebra. Vector, слайд №76Math end algebra. Vector, слайд №77Math end algebra. Vector, слайд №78Math end algebra. Vector, слайд №79Math end algebra. Vector, слайд №80Math end algebra. Vector, слайд №81Math end algebra. Vector, слайд №82Math end algebra. Vector, слайд №83Math end algebra. Vector, слайд №84Math end algebra. Vector, слайд №85Math end algebra. Vector, слайд №86Math end algebra. Vector, слайд №87Math end algebra. Vector, слайд №88Math end algebra. Vector, слайд №89Math end algebra. Vector, слайд №90Math end algebra. Vector, слайд №91Math end algebra. Vector, слайд №92Math end algebra. Vector, слайд №93Math end algebra. Vector, слайд №94
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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
Описание слайда:
MATH & ALGEBRA

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VECTOR
Описание слайда:
VECTOR

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Length Pythagorean Formula |V| = sqrt(x2 + y2)
Описание слайда:
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)
Описание слайда:
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)
Описание слайда:
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)
Описание слайда:
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
Описание слайда:
Dot Product

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Cross Product
Описание слайда:
Cross Product

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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?
Описание слайда:
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 and classes like: Vector3D Vector3DUtils Plane3D, Ray (4.0) Vector3
Описание слайда:
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/Camera Space (Point-of-view) Screen space (2D)
Описание слайда:
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
Описание слайда:
Left- and right-handed systems

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MATRICES AND SPACES
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MATRICES AND SPACES

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Matrices Matrix = Transformation placeholder So again: Local/Model matrix World matrix View/Camera matrix WVP = world * view * projection
Описание слайда:
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
Описание слайда:
Classes/Utils Matrix3D Matrix3DUtils Matrix4x4

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TRANSFORMATIONS
Описание слайда:
TRANSFORMATIONS

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Linear transformation Translation
Описание слайда:
Linear transformation Translation

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Linear transformation Scale
Описание слайда:
Linear transformation Scale

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Linear transformation Skew
Описание слайда:
Linear transformation Skew

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Linear transformation Eulers Quaternions Avoids gimbal lock Slerp (Smooth interpolated rotation) Matrix – memory intensive
Описание слайда:
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 Identity matrix
Описание слайда:
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
Описание слайда:
Nonlinear transformations Sin curve displacement Warp

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PROJECTIONS
Описание слайда:
PROJECTIONS

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Most common projections
Описание слайда:
Most common projections

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GRAPHICS PIPELINE
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GRAPHICS PIPELINE

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Programmable pipeline
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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
Описание слайда:
Stages overview

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SHADERS
Описание слайда:
SHADERS

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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
Описание слайда:
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)
Описание слайда:
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 PixelBender3D – Molehill HxSL – haXe Shader
Описание слайда:
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 Defines the final position of that vertex Outputs some variables to the Fragment shader.
Описание слайда:
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 3.2 Not available in OpenGL ES 2.0 (Molehill, webGL)
Описание слайда:
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, shadows and lights, reflections, refractions, textures, ray casting and other effects. Output is a pixel color in the format RGBA
Описание слайда:
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) Integer/Floating-point
Описание слайда:
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 techniques:
Описание слайда:
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
Описание слайда:
Let’s have a look at the WegGL implementation (click on image) three.js

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Cubemap texture
Описание слайда:
Cubemap texture

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Shader tool examples Shader Toy – WebGL MeShade – WebGL PixelBender3D – Molehill Node Based Shader Editor – Unity3D
Описание слайда:
Shader tool examples Shader Toy – WebGL MeShade – WebGL PixelBender3D – Molehill Node Based Shader Editor – Unity3D

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Interior mapping
Описание слайда:
Interior mapping

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Animations, Skin and Bones Tweens Animation controllers Blending Mixing/Additive  Vertex animations in shader Procedurally animating
Описание слайда:
Animations, Skin and Bones Tweens Animation controllers Blending Mixing/Additive  Vertex animations in shader Procedurally animating

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Animations in Away3D Broomstick
Описание слайда:
Animations in Away3D Broomstick

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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.
Описание слайда:
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 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
Описание слайда:
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
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Example

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Unitys Normal Shader Family
Описание слайда:
Unitys Normal Shader Family

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Lighting Uses normals Directional/point-lights Material settings to decide final color. Lighting is computed at each vertex. Light mapping (beast) Deferred shading
Описание слайда:
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
Описание слайда:
Lambert shading

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Real-time shadows
Описание слайда:
Real-time shadows

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Quality and performance Non realtime-shadows fastest! Shadow map resolution Number of lights
Описание слайда:
Quality and performance Non realtime-shadows fastest! Shadow map resolution Number of lights

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Example in Unity
Описание слайда:
Example in Unity

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Special effects Effects Color correction Postprocessing stage / GPU LDR/HDR, Tone mapping
Описание слайда:
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
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Physics

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Very simple physics demo
Описание слайда:
Very simple physics demo

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Frameworks Goal: Games, experimental, Vizualisation? Reach: Plugin? Multiple platforms/screens? Cost: Open source? Licenced? Support: Large community?
Описание слайда:
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 version to get all goodies Multiple screens/targets Future: Export to flash/molehill
Описание слайда:
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 the flash player. Molehill currently in alpha
Описание слайда:
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
Описание слайда:
Flash 3D Engines

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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: http://www.buraks.com/azoth/
Описание слайда:
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: http://www.buraks.com/azoth/

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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 states Probably available on iOS soon
Описание слайда:
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
Описание слайда:
WebGL Frameworks

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Jellyfish
Описание слайда:
Jellyfish

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Particles
Описание слайда:
Particles

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Hello Racer
Описание слайда:
Hello Racer

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Clouds
Описание слайда:
Clouds

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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.
Описание слайда:
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 Performance Analyzers (GPA)
Описание слайда:
Debugging Profiling CPU FlashPreloadProfiler Profiling GPU Pix for windows Intel® Graphics Performance Analyzers (GPA)

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3D Model filetypes
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3D Model filetypes

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Learning tips
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Learning tips

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Random interesting topics
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Random interesting topics

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Random interesting topics Level of detail
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Random interesting topics Level of detail

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Random interesting topics Octree, BSP Tree, Portals and Sectors
Описание слайда:
Random interesting topics Octree, BSP Tree, Portals and Sectors

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Random interesting topics Global illumination / Ambient occlusion
Описание слайда:
Random interesting topics Global illumination / Ambient occlusion

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Random interesting topics Raytracing/Raycasting/Raymarching
Описание слайда:
Random interesting topics Raytracing/Raycasting/Raymarching

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Some useful resources
Описание слайда:
Some useful resources

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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
Описание слайда:
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 third dimension. Thanks for listening! www.inear.se twitter.com/inear
Описание слайда:
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! www.inear.se twitter.com/inear

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