Inner Product Dot Product Outer Product Cross Product

  • Slides: 50
Download presentation

벡터 내적과 외적 내적(Inner Product, Dot Product) 외적(Outer Product, Cross Product) 정규화 법선벡터 =정규화

벡터 내적과 외적 내적(Inner Product, Dot Product) 외적(Outer Product, Cross Product) 정규화 법선벡터 =정규화 외적벡터 3

지엘의 후면제거 정규화 가시부피 • 법선벡터의 z 값만으로 판단가능 gl. Enable(GL_CULL_FACE); gl. Cull. Face(GL_BACK);

지엘의 후면제거 정규화 가시부피 • 법선벡터의 z 값만으로 판단가능 gl. Enable(GL_CULL_FACE); gl. Cull. Face(GL_BACK); GL_FRONT_AND_BACK gl. Disable(GL_CULL_FACE); 7

표면과 이면 그리기 모드 void gl. Polygon. Mode(GLenum face, GLenum mode) • face: 작업이

표면과 이면 그리기 모드 void gl. Polygon. Mode(GLenum face, GLenum mode) • face: 작업이 가해질 대상 면 • mode: 그리기 모드 gl. Polygon. Mode(GL_FRONT, GL_FILL); gl. Polygon. Mode(GL_BACK, GL_LINE); • GL_FRONT_AND_BACK gl. Cull. Face(GL_BACK); gl. Cull. Face(GL_FRONT); 면A를 그리지 않았을 때 11

코헨-서더런드 알고리즘 class wc. Pt 2 D { public: GLfloat x, y; }; inline

코헨-서더런드 알고리즘 class wc. Pt 2 D { public: GLfloat x, y; }; inline GLint round (const GLfloat a) { return GLint (a + 0. 5); } /* Define a four-bit code for each of the outside regions of a * rectangular clipping window. */ const GLint win. Left. Bit. Code = 0 x 1; const GLint win. Right. Bit. Code = 0 x 2; const GLint win. Bottom. Bit. Code = 0 x 4; const GLint win. Top. Bit. Code = 0 x 8; 15

코헨-서더런드 알고리즘 inline GLint inside (GLint code) { return GLint (!code); } inline GLint

코헨-서더런드 알고리즘 inline GLint inside (GLint code) { return GLint (!code); } inline GLint reject (GLint code 1, GLint code 2) { return GLint (code 1 & code 2); } inline GLint accept (GLint code 1, GLint code 2) { return GLint (!(code 1 | code 2)); } GLubyte encode (wc. Pt 2 D pt, wc. Pt 2 D win. Min, wc. Pt 2 D win. Max) { GLubyte code = 0 x 00; if (pt. x < win. Min. x) code = code | win. Left. Bit. Code; if (pt. x > win. Max. x) code = code | win. Right. Bit. Code; if (pt. y < win. Min. y) code = code | win. Bottom. Bit. Code; if (pt. y > win. Max. y) code = code | win. Top. Bit. Code; return (code); } 16

코헨-서더런드 알고리즘 void line. Clip. Coh. Suth (wc. Pt 2 D win. Min, wc.

코헨-서더런드 알고리즘 void line. Clip. Coh. Suth (wc. Pt 2 D win. Min, wc. Pt 2 D win. Max, wc. Pt 2 D p 1, wc. Pt 2 D p 2){ GLubyte code 1, code 2; GLint done = false, plot. Line = false; GLfloat m; while (!done) { code 1 = encode (p 1, win. Min, win. Max); code 2 = encode (p 2, win. Min, win. Max); if (accept (code 1, code 2)) { done = true; plot. Line = true; } else if (reject (code 1, code 2)) done = true; else { /* Label the endpoint outside the display window as p 1. */ if (inside (code 1)) { swap. Pts (&p 1, &p 2); swap. Codes (&code 1, &code 2); } 17

코헨-서더런드 알고리즘 /* Use slope m to find line-clip. Edge intersection. */ if (p

코헨-서더런드 알고리즘 /* Use slope m to find line-clip. Edge intersection. */ if (p 2. x != p 1. x) m = (p 2. y - p 1. y) / (p 2. x - p 1. x); if (code 1 & win. Left. Bit. Code) { p 1. y += (win. Min. x - p 1. x) * m; p 1. x = win. Min. x; } else if (code 1 & win. Right. Bit. Code) { p 1. y += (win. Max. x - p 1. x) * m; p 1. x = win. Max. x; } else if (code 1 & win. Bottom. Bit. Code) { /* Need to update p 1. x for nonvertical lines only. */ if (p 2. x != p 1. x) p 1. x += (win. Min. y - p 1. y) / m; p 1. y = win. Min. y; } else if (code 1 & win. Top. Bit. Code) { if (p 2. x != p 1. x) p 1. x += (win. Max. y - p 1. y) / m; p 1. y = win. Max. y; } }} 18

GL의 추가 절단면 제공 gl. Clip. Plane(GLenum plane, GLdouble *equation); gl. Enable(GLenum plane); gl.

GL의 추가 절단면 제공 gl. Clip. Plane(GLenum plane, GLdouble *equation); gl. Enable(GLenum plane); gl. Disable(GLenum plane); • plane: 절단면 식별자 GL_CLIP_PLANE 0~ GL_CLIP_PLANE 5 • equation: 평면을 나타낸는 수식의 계수가 있는 배열명 • Ax+By+Cx+D=0 Face[]={A, B, C, D} • 절단면 외부 물체가 절단되고 남는다 38

지-버퍼 알고리즘 지-버퍼(Z-Buffer) 또는 깊이버퍼(Depth Buffer) 지-버퍼 알고리즘 Initialize Frame Buffer with Background Color;

지-버퍼 알고리즘 지-버퍼(Z-Buffer) 또는 깊이버퍼(Depth Buffer) 지-버퍼 알고리즘 Initialize Frame Buffer with Background Color; Initialize Z Buffer with Infinite Distance; for Each Polygon { for Each Pixel { Calculate z of Intersection if (Calculated z < Current z of Z-Buffer) { Update Z-Buffer with Calculate z; Update Frame Buffer with the Color of Current Polygon; } } } 47

THE OUTER PLANETS The Outer Planets The OuterTHE OUTER PLANETS The Outer Planets The Outer
Planets Inner vs outer Composition inner planets arePlanets Inner vs outer Composition inner planets are
THE INNER AND OUTER PLANETS The Inner PlanetsTHE INNER AND OUTER PLANETS The Inner Planets
Inner Planets Inner and Outer Planets Space MeasurementInner Planets Inner and Outer Planets Space Measurement
Inner vs Outer Planets Inner planets are spacedInner vs Outer Planets Inner planets are spaced
Inner Planets Inner and Outer Planets Galaxies SpaceInner Planets Inner and Outer Planets Galaxies Space
The Inner and Outer Planets The Inner PlanetsThe Inner and Outer Planets The Inner Planets
The Inner Ear Inner ear anatomy Anatomy InnerThe Inner Ear Inner ear anatomy Anatomy Inner
Cross Modal Cross Cultural Cross Lingual Cross DomainCross Modal Cross Cultural Cross Lingual Cross Domain
Lewis Dot Structures Lewis Dot Structures Lewis dotLewis Dot Structures Lewis Dot Structures Lewis dot
Lewis Dot Structures Aka Dot Diagrams Electron DotLewis Dot Structures Aka Dot Diagrams Electron Dot
Lewis Dot Structures Aka Dot Diagrams Electron DotLewis Dot Structures Aka Dot Diagrams Electron Dot
Dot Plot Dot Plot A dot plot canDot Plot Dot Plot A dot plot can
DOT PAINTINGS DOT PAINTINGS Dot paintings were createdDOT PAINTINGS DOT PAINTINGS Dot paintings were created
unqualified CROSS JOIN inner qualified outer LEFT RIGHTunqualified CROSS JOIN inner qualified outer LEFT RIGHT
8 1 Inner Product Spaces Inner product Linear8 1 Inner Product Spaces Inner product Linear
25 Dot Product of Vectors Dot Product Example25 Dot Product of Vectors Dot Product Example
12 3 The Dot Product The Dot Product12 3 The Dot Product The Dot Product
The Dot Product The dot product F GThe Dot Product The dot product F G
Chapter 5 Dot Inner and Cross Products 5Chapter 5 Dot Inner and Cross Products 5
Outer SPACE An Outer Product based Sparse MatrixOuter SPACE An Outer Product based Sparse Matrix
Section 6 1 Inner Products INNER PRODUCT SPACESSection 6 1 Inner Products INNER PRODUCT SPACES
Section 3 3 Dot Product Projections THE DOTSection 3 3 Dot Product Projections THE DOT
Vectors Dot Scalar Product Think of the dotVectors Dot Scalar Product Think of the dot