Effect of applying various 2D affine transformation matrices on a unit square. Note that the reflection matrices are special cases of the scaling matrix.

Effect of applying various 2D affine transformation matrices on a unit square. Note that the reflection matrices are special cases of the scaling matrix.

Affine transformation - Wikipedia, the free encyclopedia

Affine transformation - Wikipedia, the free encyclopedia

2D affine transformation matrix - Affine transformation - Wikipedia, the free…

2D affine transformation matrix - Affine transformation - Wikipedia, the free…

Geometric Operations - Affine Transformation

Geometric Operations - Affine Transformation

An affine transformation can differentially scale the data, skew it, rotate it, and translate it. The graphic illustrates the four possible changes.

An affine transformation can differentially scale the data, skew it, rotate it, and translate it. The graphic illustrates the four possible changes.

CAAT : A javascript animation toolkit. CAAT is a multi-instance director-based scene-graph manager.  It is able to render using Canvas, WebGL and CSS with the same code base.  Features actors, containers, scene transitions, behaviors, interpolators, paths, custom affine transformation stack, timers, elements lifecycle, etc.

CAAT : A javascript animation toolkit. CAAT is a multi-instance director-based scene-graph manager. It is able to render using Canvas, WebGL and CSS with the same code base. Features actors, containers, scene transitions, behaviors, interpolators, paths, custom affine transformation stack, timers, elements lifecycle, etc.

Orthographic Projection-- (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane,[1] resulting in every plane of the scene appearing in affine transformation on the viewing surface. A lens providing an orthographic projection is known as an (object-space) telecentric lens.

Orthographic Projection-- (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane,[1] resulting in every plane of the scene appearing in affine transformation on the viewing surface. A lens providing an orthographic projection is known as an (object-space) telecentric lens.

Solve  -Δ u = f in Ω,  u = g on ∂Ω  where Ω={x|φ(Tx) < 0} with  φ(y)= (y1 - y2^2)2 + (y22+y32)-1.  T is just an affine transformation which makes sure the level-set function φ is in general position w.r.t. the mesh.    f and g are defined such that u reproduces the prescribed "solution"  upre(x)= cos(π/2x1)cos(π/2x2)cos(π/2x3).  The underlying mesh discretizes the cube (-3,3)3.

Solve -Δ u = f in Ω, u = g on ∂Ω where Ω={x|φ(Tx) < 0} with φ(y)= (y1 - y2^2)2 + (y22+y32)-1. T is just an affine transformation which makes sure the level-set function φ is in general position w.r.t. the mesh. f and g are defined such that u reproduces the prescribed "solution" upre(x)= cos(π/2x1)cos(π/2x2)cos(π/2x3). The underlying mesh discretizes the cube (-3,3)3.

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