The base class ApprQuery supports RANdom SAmple Concensus (RANSAC) for
least-squares fitting. Some of the derived classes (but not all) are
built to use the base-class support.
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Approximate a set of points by a Gaussian distribution.
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Approximate a set of points by a line. A height line in 2D is of the
form y-y0 = A*(x-x0). An orthogonal line is of the form P+t*D, where
P is a point on the line and D is a unit-length direction.
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Approximate a set of points by a plane. A height plane in 3D is of the
form z-z0 = A*(x-x0)+B*(y-y0). An orthogonal plane is of the form
Dot(N,X-P) = 0, where P is a point on the plane and N is a unit-length
normal.
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Approximate a set of 2D points by a circle or an ellipse.
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Approximate an ellipse by circular arcs. The algorithm is specific to axis-aligned
ellipses in the plane. Approximate a parametric curve by circular arcs. The algorithm
applies to any continuous parameterized curve in the plane.
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Approximate a set of 3D points by a cone. The algorithm is described
in the comments in the header file.
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Approximate an elliptical cross section and additional points by a cone.
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Approximate a set of 3D points by a cylinder.
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Approximate a set of 3D points by a torus. The algorithm is described
in the comments in the header file.
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Approximate a set of points by a curve or surface that is represented
implicitly by a quadratic equation X^T*A*X+B^T*X+C = 0, where A is NxN,
B is Nx1, and C is a scalar (N = 2 or 3). The Nx1 vector X represents
the variables. The implementation contains specialized forms when you
believe the points lie on a circle or on a sphere.
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Approximate a set of points by a sphere, ellipsoid, or paraboloid.
The PDF reference describes the algorithm and has pseudocode.
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Approximate a set of points on a sphere by a great circle or by an arc
of a great circle.
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Approximate a set of data of the form (x,w) by w = f(x), a set of data
of the form (x,y,w) by w = f(x,y), or a set of data of the form
(x,y,z,w) by w = f(x,y,z). In all cases, f is a polynomial where all
coefficients are estimated by the least-squares algorithm.
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Approximate a set of data of the form (x,w) by w = f(x), a set of data
of the form (x,y,w) by w = f(x,y), or a set of data of the form
(x,y,z,w) by w = f(x,y,z). In all cases, f is a polynomial, but the
caller specifies which of the coefficients are to be estimated by the
least-squares algorithm. For example, for degree 3, ApprPolynomia2 will
fit (x,w) data with w = c0+c1*x+c2*x^2+c3*x^3 and estimate all
coefficients c0, c1, c2, and c3. In ApprPolynomialSpecial2, the caller
can specify that w = c1*x+c3*x^3, believing that c0 and c2 are both zero.
The least-squares algorithm will estimate only c1 and c3.
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Approximate a set of points in 2D by two parallel lines.
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Fit a rectangle to a convex quadrilateral that is nearly a rectangle. The
algorithm uses a least-squares formulation.
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