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object --+ | mesh_patch_2D
2D mesh patch generator (for 4 or 8 points of a fixed distance from a central point). i.e., total number of mesh points may be 5 or 9.
Once either 5 or 9 points have been selected, this is fixed for the mesh patch instance. The central point p0 and radii r of the mesh points are mutable using the 'update' method. If shape='circle' (default), mesh points are equidistant from p0. If shape='square', mesh points are distributed around the corners and mid-sides of a square of side length 2*r.
The points are in the order p0 followed by points in 'clockwise' order in the phase plane defined by the two variable names in p0.
Functions / callable objects can be applied to all points in the mesh patch by calling the mesh patch's 'eval' method with the function. It returns an a dictionary of mesh points -> function return values.
The direction of minimum (interpolated) gradient of a functional over the mesh can be determined from the 'min_gradient_dir' method. A similar method 'max_gradient_dir' also exists.
Highly experimental class!
Rob Clewley, Jan 2007
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Inherited from |
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_s2 = 0.70710678118654757
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_mesh5 =
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_mesh9s =
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_mesh9c =
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Inherited from |
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p0 should be of type Point, r must be either a scalar or a Point giving weighted radius in each of two directions, n must be 5 or 9.
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Evaluate the function or callable object f at the mesh patch points. Returns a dictionary of mesh point index -> function value Indices are always in the same order as the Pointset attribute 'mesh' |
Find the direction of any local minima of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict. The magnitudes of these values are compared. The direction is indicated by a Point object, a relative position at the patch's characteristic radius from p0. If the functional is constant everywhere on the patch (degenerate) then a random direction is returned. If the functional is constant everywhere except at the centre, then the vector (0,0) is returned if the centre has lower value; a random vector is returned otherwise. If the functional is partially degenerate on some subset of mesh points then the optional orient and dir arguments can provide a means to select, provided the mesh resolution is sufficiently high. orient is a vector (Point object) relative to p0 orienting a "positive" direction, such that the integer dir = -1 or +1 selects one half of the mesh points on which to conduct the search. |
Find the direction of any local minima of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict. The magnitudes of these values are compared. The direction is returned as a pair containing the two closest mesh points to the direction (in mesh local coords). If the functional is constant everywhere on the patch (degenerate) then a random direction is returned. If the functional is constant everywhere except at the centre, then the vector (0,0) is returned if the centre has lower value; a random vector is returned otherwise. If the functional is partially degenerate on some subset of mesh points then the optional orient and dir arguments can provide a means to select, provided the mesh resolution is sufficiently high. orient is a vector (Point object) relative to p0 orienting a "positive" direction, such that the integer dir = -1 or +1 selects one half of the mesh points on which to conduct the search. |
Find the direction of maximum gradient of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict. The magnitudes of the values are compared. The direction is indicated by a Point object, a relative position at the patch's characteristic radius from p0. If the functional is constant everywhere on the patch (degenerate) then a random direction is returned. If the functional is constant everywhere except at the centre, then the vector (0,0) is returned if the centre has higher value; a random vector is returned otherwise. If the functional is partially degenerate on some subset of mesh points then the optional orient and dir arguments can provide a means to select, provided the mesh resolution is sufficiently high. orient is a vector (Point object) relative to p0 orienting a "positive" direction, such that the integer dir = -1 or +1 selects one half of the mesh points on which to conduct the search. |
Find the direction of maximum gradient of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict. The magnitudes of the values are compared. The direction is returned as a pair containing the two closest mesh points to the direction (in mesh local coords). If the functional is constant everywhere on the patch (degenerate) then a random direction is returned. If the functional is constant everywhere except at the centre, then the vector (0,0) is returned if the centre has higher value; a random vector is returned otherwise. If the functional is partially degenerate on some subset of mesh points then the optional orient and dir arguments can provide a means to select, provided the mesh resolution is sufficiently high. orient is a vector (Point object) relative to p0 orienting a "positive" direction, such that the integer dir = -1 or +1 selects one half of the mesh points on which to conduct the search. |
str(x)
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str(x)
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_mesh9s
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_mesh9c
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