The Face of the Fields

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When you click on one of the colors, the text and the color of the text will be set in the field. There are times when you need clear all of the fields of a layout to allow the user to enter fresh input.

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The name of this layout is OUT. When the user clicks on the Clear button, all of the fields will be cleared. When you modify fields that contain more than characters, you will need to provide additional information to force the entire face to update. Every text face contains an internal block of lines that allow it to optimize the display of the text.

How to Run the Examples

When the text is changed, the line-list face variable should be set to NONE to force all of the text in the face to be recomputed. If you don't do this, you may see text garbage in the field. This shows a large text face. The field face that is receiving the keyboard input is called the focal face. It is the input focus. The focus is normally set by the user when a field is selected with the mouse.

Clicking on the first two buttons will change the focus. Clicking on the third button will remove the focus entirely. If your interface includes multiple layouts, it is a good idea to clear the focus before changing the layout. It requires no arguments. For some types of fields, such as a password entry, you may not want to display the text that is being input.

Any field can be set to hidden input by supplying the HIDE word. Note that access to the text in this field is different too. To print the contents of the field above use:. On occasion you may need to request a string from the user. There are two predefined request functions that can help. This function allows you to request a string from the user. It will pop-up a window to accept the input. It will pop-up a window.

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Additional How-To documents will be provided to describe scrolling, resizing, and how to control tab and return behaviors. WIP Wiki 3. Built-in Styles There are three predefined text field styles: field. Used for single line input. The return and tab keys will terminate text entry and advance to the next field.

Our approach follows Pletzer and Fillmore , where it is argued that the field staggering determines the interpolation. One outcome of this paper is to clarify when linear interpolation, conservative interpolation, or their vector variants should be used. Arakawa and Lamb described the different placement of fields within cells; the staggerings of interest here are referred to as Arakawa C and D.

In Fig. This picture is adequate for the grids originally considered by Arakawa and Lamb, typically uniform latitude—longitude-based grids.

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Such grids are characterized by cells that are curvilinear in latitude—longitude coordinates, with sometimes nonorthogonal angles between cell edges. To extend the meaning of Arakawa staggering to such grids, we define Arakawa C and D as a discretized vector field where the data are attached to cell faces and edges, respectively. In addition to edges and faces, fields can also be attached to nodes and cells. For readers familiar with exterior calculus Frankel , the above nodal, edge, face, and cell fields correspond to the 0-, 1-, 2-, and 3-forms of differential geometry.

A 0-form is a scalar function of space, whereas a 1-form can be thought of as a vector field. A 2-form has as many components as a vector field in three dimensions; however, it behaves differently under a mirror reflection, prompting some to refer to it as a pseudovector or axial vector. A pseudovector arises when taking the cross product of two vectors. Taking the dot product of a pseudovector with a vector yields a pseudoscalar, a single component quantity that behaves in many respects like a scalar but changes sign under mirror reflection. Pseudoscalars are typically volume densities, and these map to 3-forms in differential geometry.

The authors are not aware of any openly available software package capable of conservatively interpolating vector fields with staggered components rows 2 and 3 , hence the focus of this article. Table 1. Different interpolation methods are required for different types of fields scalar, vector, pseudovector, and pseudoscalar in 3D. The aim of this paper is to develop interpolation methods that are suitable for vector fields attached to edges and faces.

The ideas behind vector interpolation go back to Whitney , who introduced what are now known as Whitney basis forms on triangular grids. Generalizations of those basis functions to n -dimensional hexahedral cells have been used by Pletzer and Fillmore Mimetic methods aim to preserve the mathematical identities. The novelty of this paper is to apply vector interpolation methods to Earth science grids and demonstrate how these methods satisfy mimetic properties on a cell-by-cell basis and for fractional cells.

Apart from conservation, the methods naturally handle grid distortion and data masking; they support fields that are partially valid over edges and faces. Our focus here is on two-dimensional grids at the surface of the Earth. Owing to the geometry of planets, most three-dimensional Earth grids are constructed from two-dimensional surface grids that are extruded vertically. When the target lines are at constant elevation or the target surfaces are lateral i.

In other words, horizontal and vertical interpolation weights are computed independently. The split between horizontal grid and vertical axis can be exploited by software to reduce memory footprint and execution time, and this warrants a careful treatment of the two-dimensional case. This paper is organized as follows.


In section 3 , the mimetic and conservation properties are proven. Before proceeding, some terminology needs to be clarified. Interpolation is often thought of as approximating a function on a set of target points.

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A more useful definition is to think of interpolation as a projection onto a set of n -dimensional target objects. Depending on the type of interpolation, the target objects can be points, lines, surfaces, volumes, or hypervolumes in higher-dimensional space. This definition of interpolation agrees with bilinear interpolation when the targets are points and with area-weighted conservative interpolation when targets are areas in two dimensions or volumes in three dimensions.

All interpolation methods can be written as a linear combination of field values , with interpolation weights as coefficients. Calculation of left bilinear and right conservative interpolation weights for a source grid cell dashed lines. The bilinear interpolation weight corresponding to the node on the lower left is the ratio of the shaded area over the source cell area.

The conservative interpolation weight associated with the target cell solid line is the ratio of the shaded area over the source cell area. Note that for conservative interpolation, it is often more convenient to have and represent integrated values rather than density fields, so and should be thought of as total amount of mass, energy, and so forth i. In the following, integrals of the interpolated fields are indicated with an overbar symbol, and these are always scalar quantities. In contrast, the nonintegrated interpolated fields are denoted with a tilde, and these can be either scalars or vectors, depending on the field.

The bar and the tilde quantities do not share the same units since the former are integrated over lines, surfaces, etc.


We have a strong preference for using the bar quantities whenever possible; the reason will become apparent later. For nodal fields, the integral is over a zero-dimensional object and thus simply amounts to evaluating the function on that node. We should expect the coefficients to depend on the choice of basis functions. By analogy, with bilinear and conservative interpolation, we write where T is the target: a point , line, surface, or volume. Expressions 2 — 4 are very general; they apply to all field staggerings in 3D, irrespective of the order of the interpolation scheme. Let us look at specific examples to see how these expressions work in practice.

The interpolation weight is then the linear basis function evaluated at the target point, which is the well-known formula. It happens that for the lowest-order conservative interpolation, the basis function is piecewise constant over cells and thus can be taken out of the integral when integrating over a cell. However, it is always present and should be included for higher-order conservative interpolation. To compute the interpolation weights, we need basis functions.

Recall that bilinear interpolation basis functions are attached to grid nodes, and these have the property to take the value of one on one of the cell nodes and zero on all other nodes. High-order basis functions satisfy a similar property on cell vertices and some internal nodes. This condition is critical since it allows the interpolated field to take the exact value as the target point approaches a grid vertex. Similar conditions are desirable for edge, face, and cell interpolation. The main difference is that the orthogonality conditions now involve integrals: where is the Kronecker symbol , if.

So far, general interpolation formulas for nodal-, edge-, face-, and cell-centered fields were derived in three space dimensions. In the following, only two-dimensional, horizontal geometry will be considered, with emphasis on edge and face interpolation. In the case where the field has a dependence on elevation, the interpolation will involve an additional separate calculation of vertical interpolation coefficients, which will not be described here.

The full 3D interpolation weights are then the product of horizontal and vertical interpolation weights. The separation between horizontal and vertical dimensions is warranted if the target runs parallel to the horizontal grid. A case where the current split between horizontal and vertical dimensions would not work is when the source grid uses pressure levels for its vertical axis and the target grid a terrain-following coordinate, or vice versa. Let , be some coordinates that are aligned to cell faces. These can be chosen to be the index coordinates of a structured grid or, more generally, the barycentric coordinates of the cell.

In addition, there is a vertical coordinate z , but because our main interest is in two dimensions, all surface integrals will implicitly integrate over the vertical z dimension.

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Thus, only line integrals in the — plane will survive for face interpolation. Faces and edges are the same thing in two dimensions, although the basis functions are different. For high-order interpolation, additional symbols are required as the cell objects split into subcell objects; e. Indexing of nodes, edges, and cell for a quadrilateral cell. Two symbols are attached to each cell object. The following vector low-order, basis functions can be shown to satisfy 5 : where is the Jacobian of the cell and the unit vector pointing out of the page.

In the case of orthogonal cells, the vector edge basis functions are tangential to the supporting edge and linearly decaying toward the opposite edge. The vector face basis functions are perpendicular to the face and vanishing on the opposite face. Under more general conditions, Fig. Notice that in this case, the edge basis function is no longer tangential to the supporting east cell edge. More generally, the direction of the vector edge basis function will turn and adjust so as to be perpendicular to adjacent edges at the cell vertices.

This ensures that the line integral of an edge basis function over adjacent edges remains zero; that is, the interpolation picks up line integral contributions from that edge only. The integral over the opposite edge is zero because of the linear dependency of basis function along the perpendicular direction to the edge. Also observe how the vector face basis functions rotate, this time in order to ensure that the flux integrals of the basis function over adjacent faces are zero. Edge and face vector basis functions for a nonorthogonal, curvilinear cell in 2D solid line.

To derive the interpolation weights in 4 , the line target T must be expressed in some form. A possibility is to write the target as a polyline with each segment satisfying where and are the starting point and endpoint of the segment, respectively see Fig. Equation 8 and can then be plugged into 4 to get see appendix. First, note that the weights are the same for edge and face interpolation in two dimensions.

This means lateral fluxes can be computed using the edge interpolation method. In the remainder, we will use interchangeably the terms edge and face interpolation and line and flux integrals, depending on the physical context, with the understanding that the interpolation method works the same way in both cases. The weights are the product of two terms. This term is zero if the segment is perpendicular to the edge.

The second term is a weighted average in the direction perpendicular to the edge, which gives zero if the segment is on the opposite edge. Together, these two terms ensure that the weight becomes one when the segment occupies the entire edge and zero when the segment is on any other edge. In 10 , we assumed the segments to reside entirely within the cell. Care should be taken to break the target line into subsegments if the line intersects multiple cells.

The numerical procedure then involves computing all the intersection points of the target line with the grid, creating cell-contained subsegments between each pair of intersection points. In this section, the previously derived basis functions and weights will be shown to satisfy the conservation property for the interpolated vector field given in 2. In the first case Fig. Building blocks for composing arbitrary path and surface integrals shaded areas inside a quadrilateral cell solid lines.

In the second case Fig. Butani also explained that it took the brand years to develop these masks, saying that they did rigorous testing to perfect each formula.

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Read on to learn more about each mask. They will be available for purchase on May 23 on the brand's website or through its consultants. View On One Page. Photo 0 of 5. Previous Next Start Slideshow. Customize Select the topics that interest you:.