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Topic: Hermite curves

	Implementing Curved Surface Geometry
		The downside of curves and curved surfaces is that they are perhaps the most difficult of the three methods to learn and understand.
		Unfortunately, second-degree curves will always lie in a plane, and we're working in three dimensions, so it would be better to have a space curve, a curve that isn't confined to two dimensions or less.
		A Hermite curve is a cubic curve described by its endpoints p0 and p1 and the tangent vectors at the endpoints, v0 and v1.
	www.gamasutra.com /features/20000530/sharp_pfv.htm (0 words)

	CSC418 - Lecture Topics - Curves
		Hermite curves are defined by two points and two tangent vectors.
		Hermite curve segments can be connected in a continuous fashion by ensuring that the end-point of one curve is the same as the starting point of another, as well as ensuring that the tangent vectors for this point have the same direction.
		For a Bezier curve, the conditions are that the the last two points of one curve and the first two points of the second curve are aligned.
	www.cs.toronto.edu /~faisal/teaching/notes/csc418/faisal/topics11.html (0 words)

	Cubic Hermite spline - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis a cubic Hermite spline, named in honor of Charles Hermite (Hermite is pronounced air MEET), is a third-degree spline with each polynomial of the spline in Hermite form.
		The Hermite form consists of two control points and two control tangents for each polynomial.
		The four Hermite basis functions can be defined as
	en.wikipedia.org /wiki/Hermite_curve (135 words)

	CSC 418: Parametric Curves
		The curves for y(t) and z(t) are contructed in an analogous fashion to that for x(t).
		Bezier curves are a variation of the Hermite curves.
		The points which indicate the ends of the individual curve segments and thus the join points are known as the knots.
	pubpages.unh.edu /~cs770/notes/curves.html (0 words)

	Parametric Cubic Curves
		In a slope-intercept form function, the slope of a curve is defined by the infamous three words: "rise over run." When the "run" is zero, a dimensional vortex opens and sucks you away to the outer limits.
		The simplest of the cubic curves, the Hermite form, is defined by two endpoints and the tangent vectors at these endpoints.
		, parameterizes the endpoints and tangent vectors of the Hermite curve.
	spec.winprog.org /curves (0 words)

	CMPT 361 - 97-3 - Daryl Hepting (Site not responding. Last check: 2007-10-24)
		Each curve segment is given by 3 functions, x,y, and z, which are cubic polynomials in the parameter t.
		Cubic polynomials are the lowest-degree curves which are non-planar in 3D, and which permit the curve to interpolate two specified endpoints with specified derivatives.
		Bezier curves specify the tangent vectors for the endpoints indirectly with two points that are not on the curve.
	cs.sfu.ca /~torsten/Teaching/Cmpt361/LectureNotes/HTML/08_2Dcurves-OLD (0 words)

	Introduction to Hermite Curves (Site not responding. Last check: 2007-10-24)
		Parametric curves will be the foundation for almost all of my articles in curvature and some in my animation section, too.
		Hermite curves are a form of parametric curves that give a lot more control of the curve to the artist while remaining a fairly easy-to-solve equation for a computer.
		A Hermite curve is a three-dimensional parametric curve defined by four artist-defined "control" points.
	web.ics.purdue.edu /~kmcghee/article_01.htm (0 words)

	CMPT 361: Curves
		When the curve to be approximated is smooth, it may take a large number of points to achieve a reasonable degree of accuracy, and interactive manipulation of these points is tedious.
		Parametric curves can be drawn by evaluating the curve at successive values of the parameter and connecting those points.
		Illustrated below are: the blending functions for a Hermite curve shown with the geometry matrix elements to which they apply (left), the sum of these elements for y(t) (middle) and the final curve in 2D (right).
	www.cs.sfu.ca /~torsten/Teaching/Cmpt361/LectureNotes/HTML/08_2Dcurves (0 words)

	Hermite Curve Interpolation
		Hermite curves are very easy to calculate but also very powerful.
		We'll lose some of the flexibility of the hermite curves, but as a tradeoff the curves will be much easier to use.
		They share one thing with the hermite curves: They are still cubic polynomials, but the way they are calculated is different.
	www.cubic.org /docs/hermite.htm (0 words)

	Parametric Curves
		The inverse of B_h is thus defined as the basis matrix for the hermite curve.
		As before, the basis functions are the weighting factors for the terms in the geometry vector, and are given by the product T M_h.
		In terms of the above figure, this means P1'=P4, R1'=k R4 For a Bezier curve, the conditions are that the the last two points of one curve and the first two points of the second curve are aligned.
	www.cs.helsinki.fi /group/goa/mallinnus/curves/curves.html (0 words)

	[No title]
		For example, you can vary the angle of a joint rotation using one spline curve, or you can vary the X, Y or Z coordinates of an object's position using three spline curves.
		Also, generally the way to make interesting time-varying curves is to string a number of cubic parametric curves end-to-end in time.
		We will need to define two sequences of cubic parametric curves: one sequence to control the X coordinate of the movement, and the other to control the Y coordinate of the movement.
	mrl.nyu.edu /~perlin/courses/fall2005ugrad/hw/1026.html (0 words)

	[No title]
		Ray-Triangle intersection routine (to be used in a triangle "polygon soup" raytracer to obtain simple and accurate views of the curved surface models).
		Derivation of Incremental Forward-Difference Algorithm for Cubic Bezier Curves using the Taylor Series Expansion for Polynomial Approximation (based on earlier work from last semester).
		Derivation of the Hermite curve form (based on matrices).
	www.cs.unc.edu /~hoff/projects/comp236/curves/chcklist.html (0 words)

	[No title]
		The Expansion of the deCasteljau Algorithm for Bezier Curves
		Derivation of Incremental Forward-Difference Algorithm for Cubic Bezier Curves using the Taylor Series Expansion for Polynomial Approximation
		Hermite Curve forms (curves based on or derived from Hermite forms)
	www.cs.unc.edu /~hoff/projects/comp236/curves/contents.html (0 words)

	Singularity » New TechNote series - Curve Mathematics (Site not responding. Last check: 2007-10-24)
		The examples include suggestions on enhancements and optimization as a very good learning technique is modifying an already working code.
		The series starts with Hermite curves and will eventually work its way through Beziers, splines (cardinal, Catmull-Rom, and TCB), and Nurbs.
		Some practical examples will be discussed, including an interactive demo of how to use cubic curves to interpolate between keyframes in animation.
	www.2112fx.com /blog/pivot/entry.php?id=38 (0 words)

	Geometric Modeling, 2nd Edition:0471129577:Michael E. Mortenson:eCampus.com
		It describes and compares all the important mathematical methods for modeling curves, surfaces, and solids, and shows how to transform and assemble these elements into complex models.
		Written in a style free of the jargon of special applications, this unique book focuses on the essence of geometric modeling and treats it as a discipline in its own right.
		It integrates the three important functions of geometric modeling: to represent elementary forms (i.e., curves, surfaces, and solids), to shape and assemble these into more complex forms, and to determine concomitant derivative geometric elements (i.e., intersections, offsets, and fillets).
	www.ecampus.com /bk_detail.asp?isbn=0471129577&referrer=yah04 (0 words)

	CIS881 Reading List
		Mildly interesting as a side note, but not very important to the class.
		Introduces the various parametric curves that we'll be looking at - good introduction to them but little meat; we'll come to that later.
		Material you should read as an introduction to things we'll be dealing with later.
	www.cse.ohio-state.edu /~parent/classes/784/readingList.html (0 words)

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