🗒️ Computer Graphics (19)

1. 2022.06.23 [Computer Animation] 애니메이션을 제작할 때 도움이 될 만한 사이트

   애니메이션을 제작할 때 도움이 될 만한 사이트 들어가며 애니메이션을 제작할 때 도움이 될 만한 사이트를 정리해본다. .fbx, .obj 등 여러 종류의 3D 파일들을 다운로드 받아사 사용할 수 있다. 사이트 ① Mixamo 어도비(Adobe)에서 인수한 3D 그래픽 기술 회사 무료로 캐릭터, 애니메이션 동작을 다운로드 받을 수 있다. (회원가입 필요) 바로가기 : https://www.mixamo.com/ Mixamo www.mixamo.com ② Unreal Engine Marketplace 에픽 게임즈(Epic Games)에서 운영하는 마켓 플레이스 유료 또는 무료로 3D 모델을 다운로드 받을 수 있다. (회원가입 필요) 매달 새로운 3D 모델 파일들을 무료로 받을 수 있다. 바로가기 : https:..
2. 2022.05.01 [Computer Animation] Quaternion Catmull-Rom Spline

   Quaternion Catmull-Rom Spline Quaternion(사원수) Operations Unit Quaternion Algebra Unit Quaternion space is closed under multiplication and inverse, but not closed under addition and subtraction Rotation Quaternion Exp and Log Scale Quaternion Catmull-Rom Spline Quaternion Bezier Quaternion Bezier Curve Linear Combination of quaternion? De Casteljau by Slerp by De Casteljau Algorithm Multi-linear ..
3. 2022.05.01 [Computer Animation] De Casteljau Algorithm

   De Casteljau Algorithm Bezier Curve Review Cubic polynomial in Bernstein Bases End point Interpolation $p(0) = b_{0}$ $p(1) = b_{3}$ The tangent vectors to the curve at the end points are coincident with the first and last edges of the control point polygon $p'(0) = 3(b_{1} - b_{0})$ $p'(1) = 3(b_{3} - b_{2})$ Bezier Curve De Casteljau Algorithm(드 카스텔조 알고리즘) Alternative way for evaluating a poin..
4. 2022.05.01 [Computer Animation] B-Spline

   B-Spline B-Splines Is it possible to achieve both $C^{2}$-continuity and local controllability? B-splines can do! Uniform cubic B-spline basis functions Uniform B-spline basis functions Bell-shaped basis function for each control points Overlapping basis functions Control points correspond to knot points Uniform B-splines We have $(n+1)+2$ unknowns. B-spline Properties Variation Diminishing $C^{..
5. 2022.05.01 [Computer Animation] Natural Cubic Spline

   Natural Cubic Spline Natural Cubic Splines $C^{n-1}$-continuity can be achieved from splines of degree $n$. Cubic Splines can have $C^{2}$-continuity. We have $4n$ unknowns. $n$ cubic segments (4 coefficients for each segment) We have $4n$ unknowns $n$ cubic segments (4 coefficients for each segment) We have $(4n-2)$ equations $2n$ equations for end point interpolation $(n-1)$ equations for tang..
6. 2022.05.01 [Computer Animation] Catmull-Rom Spline

   Catmull-Rom Spline Without tangent vectors? Cubic Splines τ(타우) 값에 따른 그래프의 변화 Catmull-Rom Spline Properties Variation Diminishing the curve in 2D space does not oscillate about any straight line more often than the control point polygon. $C^{1}$-continuity Local Controllability Question Find a catmull-rom cubic spline interpolating the four key points with $\tau = 0.5$ $p(t) = L_{0}(t)p_{0} + L_..
7. 2022.05.01 [Computer Animation] Bezier Curve & Bezier Spline

   Bezier Curve & Bezier Spline Basic Functions A linear space of cubic polynomials Monomial basis $(t^{3}, t^{2}, t^{1}, t^{0}$ $x(t) = a_{3}t^{3} + a_{2}t^{2} + a_{1}t + a_{0}$ The coefficients $a_{i}$ do not give tangible(유형의) geometric meaning. Bezier Control Points Control Points $b_{0}, b_{1}, b_{2}, b_{3}$ Demo http://blogs.sitepointstatic.com/examples/tech/canvas-curves/bezier-curve.html Ca..
8. 2022.05.01 [Computer Animation] Keyframing and Splines

   Keyframing and Splines What is Motion? Motion is a time-varying transformation from body local system to world coordinate system. (in a very narrow sense) Transformation Rigid Transformation(강체 변환) Rotate + Translate 3x3 orthogonal matrix + 3-vector $T : x → Rx + b$ Affine Transformation(어파인 변환) Scale + Shear + Rigid Transformation 3x3 matrix + 3-vector $T: x → Ax + b$ Homogeneous Transformation..
9. 2022.04.24 [Unreal Engine 4] 블루프린트 클래스(Blueprint Class)에 Static Mesh 연결하기

   블루프린트 클래스(Blueprint Class)에 Static Mesh 연결하기 개요 블루프린트 클래스(Blueprint Class)를 생성한 후, Static Mesh를 연결해보자. 방법 블루프린트 클래스(Blueprint Class)를 생성한다. 생성한 블루프린트 클래스에 이름을 넣어주고, 더블 클릭을 하여 블루프린트 클래스 편집창에 진입한다. [Add Component] 버튼을 클릭한 후, "Static Mesh" 를 검색한 후 불러온다. 오른쪽의 [Details] 창에서 [Static Mesh]를 설정해준다. (원하는 액터를 지정해주면 된다.) 결과 Static Mesh가 적용된 블루프린트 클래스를 확인할 수 있다.
10. 2022.04.16 [Unreal Engine 4] 새로운 월드 생성 & 기본 환경 설정

    새로운 월드 생성 & 기본 환경 설정 개요 언리얼 엔진 4(Unreal Engine 4)에서 새로운 월드를 생성하고, 기본 환경을 설정하는 과정을 알아보자. 방법 ① 새로운 레벨(Level) 생성하기 [Add/Import] 버튼을 누른 후 [Level] 항목을 선택한다. 그리고 파일 이름을 지정해준다. 그리고 생성된 파일을 더블 클릭해서 월드에 진입한다. ② 대기 환경 생성하기 하늘(Sky) 생성하기 [Place Actors] 탭의 검색창에 "bp"를 검색해서, 요소를 마우스로 드래그(Drag)한 후, 월드(검정색 화면)에 드롭(Drop) 해준다. 월드에는 아직 아무런 광원이 존재하지 않기 때문에 까맣게 나온다. 태양(Sun) 생성하기 [Place Actors] 탭의 검색창에 "dir"를 검색해서, 요소..
11. 2022.04.10 [Computer Animation] Slerp(Spherical Linear Interpolation)

    Slerp(Spherical Linear Interpolation) Interpolation betwee two orientations, $o_{a}$ and $o_{b}$? $o_{a}$ and $o_{b}$ can be represented by Euler-angles 3x3 matrices quaternions How can them be interpolated? Is the linear interpolation applicable? When the axis-angle is known, $o_{a} → o_{b}$ Rotation between two orientations? Rotation between two SO(3) matrices, $m_{a}$ and $m_{b}$ $m_{r} = m_{..
12. 2022.04.10 [Computer Animation] 3D Rotation and Orientation

    3D Rotation and Orientation Orientation vs. Rotation Rotation Circular movement Orientation The state of being oriented. Given a coordinate system, the orientation of an object can be represented as a rotation from a reference pose. Analogy (point : vector) is similar to (orientation : rotation) Both represent a sort of (state : movement) What is 3D Rotation? Many different ways to describe Rota..
13. 2022.04.03 [Computer Animation] 2D Rotation and Orientation

    2D Rotation and Orientation Orientation vs. Rotation Rotation Circular movement. Orientation The state of being oriented. Given a coordinate system, the orientation of an object can be represented as a rotation from a reference pose. Analogy (point : vector) is similar to (orientation : rotation) Both represent a sort of (state : movement) Representations for 2D rotations and orientations Turnin..
14. 2022.03.26 [Computer Animation] Linear Interpolation

    Linear Interpolation(선형 보간법) 보간법(Interpolation) : 함수의, 둘 이상의 변숫값에 대한 함숫값을 알고, 그것들 사이의 임의의 변숫값에 대한 함숫값 내지는 그 근삿값을 구하는 계산법 - Oxford Languages 1D Linear Interpolation What is the function, $f(t)$, such that $\begin{matrix} 0 ≤ t ≤ 1 \\ f(0) = 1 \\ f(1) = 5 \end{matrix} ?$ If $f(t)$ is a Linear Equation, $f(t) = at + b$ 2 Unknowns, 2 Equations $\begin{matrix} 1 = a · 0 + b \\ 5 = a · 1 + b \end{matr..
15. 2022.03.26 [Computer Animation] Geometric Transformations

    Geometric Transformations Geometric Transformation, $\mathbb{T}$ $\mathbb{T}$ is a function Geometric structure A → Geometric structure B A geo. structure is represented by a set of points or vectors in 2D o 3D in the general case. 2D Examples Scaling ● Scale by 2 in the y-axis. → $S(1, 2)$ ▶ $x^{'} = x$ ▶ $y^{'} = 2y$ ● Scale by 0.5 in the x-axis. → $S(0.5, 1)$ ▶ $x^{'} = 0.5x$ ▶ $y^{'} = y$ ● ..
16. 2022.03.15 [Computer Animation] Vector Operations

    Vector Operations Scalar vs. Vector Scalar : a quantity, such as time or temperature, that has magnitude(규모) but not direction. Vector : a variable quantity, such as force, that has size and direction. Scalar vs. Vector vs. Matrix Addition and Scalar Multiplication Let $a$ and $b$ be 3D Vectors and $s$ is a scalar value. Vector Addition Vector-Scalar Multiplication Vector Length (Magnitude) Unit..
17. 2022.03.15 [Computer Animation] Point and Vector (Affine Geometry)

    Point and Vector (Affine Geometry) Animation Function of time Movement 1D Space Uniform Speed Non-Uniform Speed 2D or 3D Space Cartesian Coordinate System(데카르트 좌표계) 를 사용하여 표현한다. 함수가 만들어지는 절차 Sampling Global Points In a New Coordinates System Sampling Difference Vectors In a New Coordinates System Function Points and Vectors Points and Vectors A Point is a position specified with coordinate value..
18. 2022.03.08 [Computer Animation] History of Animation

    History of Animation Early Animation Devices Filpbooks Stop Motion (Puppet, Clay) Cel Animation Chalk Animation Silhouette Animation A Brief History of Animation 1877 : Emile Reynaud invented the Praxinoscope 1889 : Emile Reynaud invented Theatre Optique 1893 : Edison invtented the Kinetoscope Only one viewer at a time 1894 : Lumiere invented the cinematograph Camera + Projector + Printer 1900 :..
19. 2022.03.03 [Computer Animation] Computer Animation

    Computer Animation Animate to give life to or cause to come alive to make lively; enliven to encourage or inspire to impart motion to; move to action or work to record on film or video tape so as to give movement to => an animated cartoon Animatronics Animation + Electronics 특수 효과 기술의 일종으로, 생물을 모방한 로봇을 사용하여 촬영하는 기술 Animation A way of making a movie by using a series of drawings, computer graphic..