#SEQUENCE OF TRANSFORMATIONS HOW TO#
#SEQUENCE OF TRANSFORMATIONS CODE#

Also, guidelines for the application of Levin-type sequence transformations are discussed, and a few numerical examples are given. How to apply a sequence of transformations to a function, and a look at when the order of transformations matters and when it. For important special cases, extensions of the general results are presented. The sequence of transformation is 90 degrees counterclockwise rotation, followed by a horizontal translation to the right by 2 units The ordered pair-rule for. Common properties and results on convergence acceleration and stability are given. So we first do a translation, then we do a reflection over a horizontal line, PQ, then we do vertical stretch about PQ. As illustration, two new sequence transformations are derived. They say a sequence of transformations is described below. It is discussed how such transformations may be constructed by either a model sequence approach or by iteration of simple transformations. Here, we review known Levin-type sequence transformations and put them in a common theoretical framework. Special cases of such Levin-type transformations belong to the most powerful currently known extrapolation methods for scalar sequences and series. Some methods of automatic selection of sequence transformations for accelerating the convergence of sequences are presented. Then, nonlinear sequence transformations are obtained. Sequence transformations include linear mappings such as. After a vertical shrink by a factor of 5, the. As shown first by Levin, it is possible to obtain such asymptotic information easily for large classes of sequences in such a way that the ω n are simple functions of a few sequence elements s n. In mathematics, a sequence transformation is an operator acting on a given space of sequences. After a horizontal stretch by factor 1/5, the transformed function becomes 1/5 x2 +1/5 x at a point (5x,y). Such remainder estimates provide an easy-to-use possibility to use asymptotic information on the problem sequence for the construction of highly efficient sequence transformations. Key Points: A translation is an isometry where all points in the preimage are moved parallel to a given line. The basic idea is to construct from a given sequence ) that depend not only on the sequence elements or partial sums s n but also on an auxiliary sequence of the so-called remainder estimates ω n are of Levin-type if they are linear in the s n, and nonlinear in the ω n. LO-9 Sequences of Transformations.notebook.

#SEQUENCE OF TRANSFORMATIONS CODE#

Output.Position = mul(viewPosition, Projection) įinally (and this is optional but might be usefull for others wondering the same), how would you write the HLSL code to do this projective texturing multiplication or how would you do the transformations if you passed the complete Matrix via XNA.Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. As stated in 44, the so-called Shanks transformation is arguably the best all-purpose method for accelerating convergence of sequences. This is because I learned to read matrix multiplication from left to right and also because I thought the sequence of transformations should go in this order:īecause Matrix multiplication is not commutative, what is the order I should do the multiplications in?Īnd if it is indeed in the same order as the sequence of transformations of normal objects, why is it written like this?īy the same order of sequence I mean something like this hlsl code: float4 worldPosition = mul(input.Position, World) įloat4 viewPosition = mul(worldPosition, View) tgtf genderbender pinkhairgirl sequence swimsuit transformation transgender. The order in which the transformations are written confused me. Visit Amazing Transformation Comics(link is external) We are a comics site. When I was reading this article on Projective Texturing (9.3.2) on nvidia, I came across this graph:

Sequence of transformations