Geometric Transformations - UC Homepages
sedirection).Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo TfmsFigure: RotatingR2 by θ radians4/8
Rotations in R2RA rotation of R2 by θ is the map R2 R2 defined by letting R( x ) be thevector obtained by rotating x (about 0) by θ radians (in the clockwisedirection). xApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo TfmsFigure: RotatingR2 by θ radians4/8
Rotations in R2RA rotation of R2 by θ is the map R2 R2 defined by letting R( x ) be thevector obtained by rotating x (about 0) by θ radians (in the clockwisedirection). xθApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo TfmsFigure: RotatingR2 by θ radians4/8
Rotations in R2RA rotation of R2 by θ is the map R2 R2 defined by letting R( x ) be thevector obtained by rotating x (about 0) by θ radians (in the clockwisedirection).R( x ) xθApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo TfmsFigure: RotatingR2 by θ radians4/8
Rotations in R2RA rotation of R2 by θ is the map R2 R2 defined by letting R( x ) be thevector obtained by rotating x (about 0) by θ radians (in the clockwisedirection).R( x ) xθApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo TfmsFigure: RotatingR2 by θ radians4/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L;Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms5/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L; L is some fixed line in R2 .Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms5/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L; L is some fixed line in R2 .Reflection across the x-axis is x R yy xyxApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms5/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L; L is some fixed line in R2 .Reflection across the x-axis is x xR .y yy xyx x yApplied Linear Algebra Linear TfmsChapter 3, Section 6, Geo Tfms5/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L; L is some fixed line in R2 .Reflection across the x-axis is x xR .y yy x xReflection across the y -axis isyy xx R .xyy x yApplied Linear Algebra Linear TfmsChapter 3, Section 6, Geo Tfms5/8
Reflections in R2RThe reflection R2 R2 across L is given by letting R( x ) be the vectorobtained by reflecting x across the line L; L is some fixed line in R2 .Reflection across the x-axis is x xR .y yy x xReflection across the y -axis isyy xx R .xyy x y Reflection across the line y x is x yR .yxApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms5/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL;Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms6/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL; L is some fixed line in R2 .Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms6/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL; L is some fixed line in R2 .Projection onto the x-axis is yx P xyyxApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms6/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL; L is some fixed line in R2 .Projection onto the x-axis is yx x P .xy0y xx0Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms6/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL; L is some fixed line in R2 .Projection onto the x-axis is yx x P .x0y0yyProjection onto the y -axis is xx 0x 0P .yyApplied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms6/8
Projections in R2PThe projection R2 R2 onto L is given by letting P( x ) be the vectorobtained by orthogonally projecting x onto the direction vector for the lineL; L is some fixed line in R2 .Projection onto the x-axis is yx x P .x0y0yyProjection onto the y -axis is xx 0x 0P .yyProjection onto the line y x,We will discuss projections at greatlength in Chapter 6!Applied Linear Algebra x x y 1P .y12Linear TfmsChapter 3, Section 6, Geo Tfms6/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector.Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector.u Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xu Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xu Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xu Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xp u Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xThe orthogonal projection of x onto u is the pictured vector p p u Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. xp The orthogonal projection of x onto u is the pictured vector p which is parallelto u (so, p s u for some scalar) andhas the property thatu Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. x zp The orthogonal projection of x onto u is the pictured vector p which is parallelto u (so, p s u for some scalar) andhas the property that z x p u .u Applied Linear AlgebraLinear TfmsChapter 3, Section 6, Geo Tfms7/8
Orthogonal Projection Onto a VectorLet u be a fixed vector, and x a variable vector. x zp u Applied Linear AlgebraThe orthogonal projection of x onto u is the pictured vector p which is parallelto u (so, p s u for some scalar) andhas the property that z x p u .In Chapter 6 we will see that it is easyto determine s.Linear TfmsChapter 3, Section 6, Geo Tfms7/8
Geometric Transformations These are transformations R2!R2 that include translations dilations rotations re ections projections shearing By using compositions of these, we can create all sorts of transformations. Many of the above can also be de ned as maps Rn!Rn. Applied Linear
transformations performing geometric exchanges based on the vertical and horizontal locations. The performance of the geometric transformations on quantum images, GI, is based on the function, G, on the computational basis vectors. The general structure of circuits for geometric transformations
Geometric transformations Geometric transformations will map points in one space to points in another: (x',y',z') f(x,y,z). These transformations can be very simple, such as scaling each coordinate, or complex, such as non-linear twists and bends. We'll focus on transformations that ca
Geometric Transformations Changes in size, shape are accomplished with geometric transformation. It alter the coordinate descriptions of object. The basic transformations are Translation, Roatation, Scaling. Other transformations are Reflection and shear.Basic transformations u
level of abstraction and look at how geometric transformations are used to alter the view of a 2D model: how we can translate, scale, and rotate the model, and how transformations affect what the viewport 'sees' Geometric Transformations Secti
Infor Ming.le Homepages A key feature of Infor CloudSuite is the ability to create, curate, and use collections of high level views into a user's work. These collections are pre-sented as "homepages". Infor Ming.le provides the framework in which homepages can be created,
GeorgiaFIRST Financials Fluid Homepages Job Aid . FLUID HOMEPAGES IN PEOPLESOFT FINANCIALS . The Fluid Interface is designed to adapt easily to various devices including mobile phones and tablets. The Fluid homepage pictured below replaces the Classic homepage that displayed the navigation menu on the left side.
The formula for the sum of a geometric series can also be written as Sn a 1 1 nr 1 r. A geometric series is the indicated sum of the terms of a geometric sequence. The lists below show some examples of geometric sequences and their corresponding series. Geometric Sequence Geometric Series 3, 9, 27, 81, 243 3 9 27 81 243 16, 4, 1, 1 4, 1 1 6 16 .
Anatomy Fig 1. Upper limb venous anatomy [1] Vessel Selection Right arm preferable to left (as the catheter is more likely to advance into the correct vessel), vessel selection in order: 1. Basilic 2. Brachial 3. Cephalic Pre-procedure Patient information and consent Purpose of procedure, risks, benefits, alternatives. Line care: Consider using local patient information leaflet as available .
