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dc.contributor.authorHadfield, Hugo
dc.contributor.authorAchawal, Sushant
dc.contributor.authorLasenby, Joan
dc.contributor.authorLasenby, Anthony
dc.contributor.authorYoung, Benjamin
dc.date.accessioned2021-02-11T16:16:49Z
dc.date.available2021-02-11T16:16:49Z
dc.date.issued2021-02-11
dc.date.submitted2019-10-31
dc.identifier.issn0188-7009
dc.identifier.others00006-021-01117-8
dc.identifier.other1117
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/317496
dc.descriptionFunder: Natural Environment Research Council; doi: http://dx.doi.org/10.13039/501100000270
dc.description.abstractAbstract: Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes.
dc.languageen
dc.publisherSpringer International Publishing
dc.rightsAttribution 4.0 International (CC BY 4.0)en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subjectArticle
dc.subjectT.C. : ENGAGE 2019- Geometric Algebra for Computing, Graphics & Engineering
dc.subjectConformal geometric algebra
dc.subjectRay-tracing
dc.subjectDirect object interpolation
dc.subjectSurface curvature
dc.subjectMesh geometry
dc.subjectPrimary 99Z99
dc.subjectSecondary 00A00
dc.titleExploring Novel Surface Representations via an Experimental Ray-Tracer in CGA
dc.typeArticle
dc.date.updated2021-02-11T16:16:49Z
prism.issueIdentifier2
prism.publicationNameAdvances in Applied Clifford Algebras
prism.volume31
dc.identifier.doi10.17863/CAM.64612
dcterms.dateAccepted2021-01-06
rioxxterms.versionofrecord10.1007/s00006-021-01117-8
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidHadfield, Hugo [0000-0003-4318-050X]
dc.identifier.eissn1661-4909
pubs.funder-project-idEngineering and Physical Sciences Research Council (1949701)


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)