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.

File:2D affine transformation matrix.svg - Wikimedia Commons

File:2D affine transformation matrix.svg - Wikimedia Commons

Geometric Operations - Affine Transformation

Geometric Operations - Affine Transformation

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…

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.

https://flic.kr/p/xbBgpc | Waning Gibbous Moon 201509020701 | Waning Gibbous Moon from Austin Texas on the night of Sept 1.  Questar 3.5" with Sony NEX-5N at prime focus.  ISO 400 for 1/80 sec.  34 frames aligned and stacked with 8 parameter affine transformation in Nebulosity, deconvolved in Lynkeos, with HDR exposure stretching in Photoshop.

https://flic.kr/p/xbBgpc | Waning Gibbous Moon 201509020701 | Waning Gibbous Moon from Austin Texas on the night of Sept 1. Questar 3.5" with Sony NEX-5N at prime focus. ISO 400 for 1/80 sec. 34 frames aligned and stacked with 8 parameter affine transformation in Nebulosity, deconvolved in Lynkeos, with HDR exposure stretching in Photoshop.

Maths - Affine Transformations

Maths - Affine Transformations

1ucasvb:  Affine transformations preserve parallel lines, and include rotations, scaling, shears and translations. Linear transformations can’t perform translations, but this can be achieved if we go to a higher dimension.  In this animation, a planar (2D) shape lying on the plane z = 1 is translated by means of a linear transformation in three dimensions: a shear along the z axis.  Rotations can be performed normally, also around the z axis. For rotations around any other axis parallel to…

1ucasvb: Affine transformations preserve parallel lines, and include rotations, scaling, shears and translations. Linear transformations can’t perform translations, but this can be achieved if we go to a higher dimension. In this animation, a planar (2D) shape lying on the plane z = 1 is translated by means of a linear transformation in three dimensions: a shear along the z axis. Rotations can be performed normally, also around the z axis. For rotations around any other axis parallel to…

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.

Understanding Affine Transformations With Matrix Mathematics

Understanding Affine Transformations With Matrix Mathematics

Wildberger in his lecture series on linear algebra, I intend to implement his mathematical ideas with Flash. We shall not delve into the mathematical manipulation of matrices.

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