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Local Polynomial Interpolation Tool

أداة الاستيفاء متعدد الحدود المحلي

ArcMap ArcGIS

How to use Local Polynomial Interpolation Tool in ArcToolbox ArcMap ArcGIS??

كيفية استخدام أداة الاستيفاء متعدد الحدود المحلي ؟؟

Path to access the toolمسار الوصول الى الأداة

:

Local Polynomial Interpolation Tool, Interpolation Toolset, Geostatistical Analyst Tools Toolbox

 

Local Polynomial Interpolation

Fits the specified order (zero, first, second, third, and so on) polynomial, each within specified overlapping neighborhoods, to produce an output surface.

يناسب الترتيب المحدد (صفر ، أول ، ثاني ، ثالث ، وهكذا) متعدد الحدود ، كل منها ضمن الأحياء المتداخلة المحددة ، لإنتاج سطح ناتج.

1.    Input features أدخل المعالم

The input point features containing the z-values to be interpolated.

معالم نقطة الإدخال التي تحتوي على قيم z المطلوب استكمالها.

Z value field

Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain z-values or m-values.

Output geostatistical layer (optional)

The geostatistical layer produced. This layer is required output only if no output raster is requested.

Output raster (optional)

The output raster. This raster is required output only if no output geostatistical layer is requested.

Output cell size (optional)

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings.

If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

Order of polynomial (optional)

The order of the polynomial.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

2.    Z value field حقل قيمة الإرتفاع

Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain z-values or m-values.

الحقل الذي يحتوي على قيمة ارتفاع أو مقدار لكل نقطة. يمكن أن يكون هذا حقلاً رقميًا أو حقل الشكل إذا كانت ميزات الإدخال تحتوي على قيم z أو قيم m.

Output geostatistical layer (optional)

The geostatistical layer produced. This layer is required output only if no output raster is requested.

Output raster (optional)

The output raster. This raster is required output only if no output geostatistical layer is requested.

Output cell size (optional)

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings.

If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

Order of polynomial (optional)

The order of the polynomial.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

3.    Output geostatistical layer (optional) طبقة إحصائية الإخراج (اختياري)

The geostatistical layer produced. This layer is required output only if no output raster is requested.

أنتجت الطبقة الجيوإحصائية. هذه الطبقة مطلوبة فقط في حالة عدم طلب الناتج النقطي.

Output raster (optional)

The output raster. This raster is required output only if no output geostatistical layer is requested.

Output cell size (optional)

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings.

If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

Order of polynomial (optional)

The order of the polynomial.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

4.    Output raster (optional) النقطية المخرجة (اختياري)

The output raster. This raster is required output only if no output geostatistical layer is requested.

النقطية الإخراج. مطلوب إخراج هذا النقطية فقط في حالة عدم طلب طبقة إحصائية جغرافية ناتجة.

Output cell size (optional)

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings.

If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

Order of polynomial (optional)

The order of the polynomial.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

5.    Output cell size (optional) حجم خلية الإخراج (اختياري)

The cell size at which the output raster will be created.

This value can be explicitly set under Raster Analysis from the Environment Settings.

If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.

حجم الخلية التي سيتم إنشاء البيانات النقطية للإخراج بها.

يمكن تعيين هذه القيمة بشكل صريح ضمن تحليل البيانات النقطية من إعدادات البيئة.

إذا لم يتم تعيينه ، فهو أقصر عرض أو ارتفاع مدى معالم نقطة الإدخال ، في الإسناد المكاني للإدخال ، مقسومًا على 250.

Order of polynomial (optional)

The order of the polynomial.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

6.    Order of polynomial (optional) ترتيب كثير الحدود (اختياري)

The order of the polynomial.

ترتيب كثير الحدود.

Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth

·      Major semiaxis—The major semiaxis value of the searching neighborhood.

·      Minor semiaxis—The minor semiaxis value of the searching neighborhood.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Standard Circular

·      Radius—The length of the radius of the search circle.

·      Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.

·      Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.

·      Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.

·      Sector type—The geometry of the neighborhood.

o   One sector—Single ellipse.

o   Four sectors—Ellipse divided into four sectors.

o   Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.

o   Eight sectors—Ellipse divided into eight sectors.

Smooth Circular

·      Radius—The length of the radius of the search circle.

·      Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

7.    Search neighborhood (optional) البحث في الحي (اختياري)

يحدد النقاط المحيطة التي سيتم استخدامها للتحكم في الإخراج. المعيار هو الافتراضي.

اساسي

• المحور الرئيسي - القيمة المحورية الرئيسية لحي البحث.

• المحاور الصغرى - القيمة المحورية الصغرى لحي البحث.

• الزاوية - زاوية الدوران للمحور (الدائرة) أو المحور شبه الرئيسي (القطع الناقص) للنافذة المتحركة.

• الحد الأقصى من الجيران - الحد الأقصى لعدد الجيران الذي سيتم استخدامه لتقدير القيمة في موقع غير معروف.

• الحد الأدنى من الجيران - الحد الأدنى لعدد الجيران الذي سيتم استخدامه لتقدير القيمة في موقع غير معروف.

• نوع القطاع - هندسة الحي.

o قطاع واحد - قطع ناقص مفرد.

o أربعة قطاعات - Ellipse مقسمة إلى أربعة قطاعات.

o أربعة قطاعات متغيرة — Ellipse مقسمة إلى أربعة قطاعات ومزاحة 45 درجة.

o ثمانية قطاعات - Ellipse مقسمة إلى ثمانية قطاعات.

ناعم

• المحور الرئيسي - القيمة المحورية الرئيسية لحي البحث.

• المحاور الصغرى - القيمة المحورية الصغرى لحي البحث.

• الزاوية - زاوية الدوران للمحور (الدائرة) أو المحور شبه الرئيسي (القطع الناقص) للنافذة المتحركة.

• عامل التجانس - يُنشئ خيار الاستيفاء المتجانس شكلًا بيضاويًا خارجيًا وقطعًا داخليًا على مسافة مساوية لـ Semiaxis الرئيسي مضروبًا في عامل التنعيم. النقاط التي تقع خارج أصغر شكل بيضاوي ولكن داخل أكبر قطع ناقص يتم ترجيحها باستخدام دالة سينية بقيمة بين صفر وواحد.

التعميم القياسي

• نصف القطر - طول نصف قطر دائرة البحث.

• الزاوية - زاوية الدوران للمحور (الدائرة) أو المحور شبه الرئيسي (القطع الناقص) للنافذة المتحركة.

• الحد الأقصى من الجيران - الحد الأقصى لعدد الجيران الذي سيتم استخدامه لتقدير القيمة في موقع غير معروف.

• الحد الأدنى من الجيران - الحد الأدنى لعدد الجيران الذي سيتم استخدامه لتقدير القيمة في موقع غير معروف.

• نوع القطاع - هندسة الحي.

o قطاع واحد - قطع ناقص مفرد.

o أربعة قطاعات - Ellipse مقسمة إلى أربعة قطاعات.

o أربعة قطاعات متغيرة — Ellipse مقسمة إلى أربعة قطاعات ومزاحة 45 درجة.

o ثمانية قطاعات - Ellipse مقسمة إلى ثمانية قطاعات.

دائري ناعم

• نصف القطر - طول نصف قطر دائرة البحث.

• عامل التجانس - يُنشئ خيار الاستيفاء المتجانس شكلًا بيضاويًا خارجيًا وقطعًا داخليًا على مسافة مساوية لـ Semiaxis الرئيسي مضروبًا في عامل التنعيم. النقاط التي تقع خارج أصغر شكل بيضاوي ولكن داخل أكبر قطع ناقص يتم ترجيحها باستخدام دالة سينية بقيمة بين صفر وواحد.

Kernel function (optional)

The kernel function used in the simulation.

·      EXPONENTIAL—The function grows or decays proportionally.

·      GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

·      QUARTIC—Fourth-order polynomial function.

·      EPANECHNIKOV—A discontinuous parabolic function.

·      POLYNOMIAL5—Fifth-order polynomial function.

·      CONSTANT—An indicator function.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

8.    Kernel function (optional) وظيفة النواة (اختياري)

The kernel function used in the simulation.

· EXPONENTIAL—The function grows or decays proportionally.

· GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.

· QUARTIC—Fourth-order polynomial function.

· EPANECHNIKOV—A discontinuous parabolic function.

· POLYNOMIAL5—Fifth-order polynomial function.

· CONSTANT—An indicator function.

دالة النواة المستخدمة في المحاكاة.

• EXPONENTIAL - تنمو الوظيفة أو تتلاشى بشكل متناسب.

• GAUSSIAN - وظيفة على شكل جرس تسقط بسرعة نحو زائد أو ناقص اللانهاية.

• QUARTIC - دالة كثيرة حدود من الدرجة الرابعة.

• EPANECHNIKOV - وظيفة قطع مكافئ متقطع.

• POLYNOMIAL5 - دالة كثيرة الحدود من الدرجة الخامسة.

• ثابت - وظيفة مؤشر.

Bandwidth (optional)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

·      Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

·      Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

·      PREDICTION—Prediction surfaces are produced from the interpolated values.

·      PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

·      CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

9.    Bandwidth (optional) عرض النطاق الترددي (اختياري)

Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

يستخدم لتحديد أقصى مسافة تستخدم عندها نقاط البيانات للتنبؤ. مع زيادة عرض النطاق الترددي ، يزداد تحيز التنبؤ ويقل تباين التنبؤ.

Use spatial condition number threshold (optional)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

· Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

· Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

· PREDICTION—Prediction surfaces are produced from the interpolated values.

· PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

· CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

10. Use spatial condition number threshold (optional) استخدم حد رقم الحالة المكانية (اختياري)

Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

· Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.

· Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

خيار للتحكم في إنشاء التنبؤ والتنبؤ بالأخطاء المعيارية حيث تكون التنبؤات غير مستقرة. هذا الخيار متاح فقط لكثيرات الحدود من الرتب 1 و 2 و 3.

• بدون رادع - سيتم إنشاء التنبؤات في كل مكان ، بما في ذلك المناطق التي تكون فيها التوقعات غير مستقرة. هذا هو الافتراضي.

• تم التحقق - لن يتم إنشاء التنبؤ والتنبؤ بالأخطاء المعيارية عندما تكون التنبؤات غير مستقرة.

Spatial condition number threshold (optional)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

· PREDICTION—Prediction surfaces are produced from the interpolated values.

· PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

· CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

11. Spatial condition number threshold (optional) حد رقم الحالة المكانية (اختياري)

Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

تحتوي كل مصفوفة مربعة قابلة للانعكاس على رقم شرط يشير إلى مدى دقة حل المعادلات الخطية مع تغيير بسيط في معاملات المصفوفة (يمكن أن يكون ذلك بسبب عدم دقة البيانات). إذا كان رقم الشرط كبيرًا ، فإن تغييرًا بسيطًا في معاملات المصفوفة ينتج عنه تغيير كبير في متجه الحل.

Weight field (optional)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

Output surface type (optional)

Surface type to store the interpolation results.

· PREDICTION—Prediction surfaces are produced from the interpolated values.

· PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

· CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

12. Weight field (optional) حقل الوزن (اختياري)

Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

تستخدم للتأكيد على الملاحظة. كلما زاد الوزن ، زاد تأثيره على التنبؤ. بالنسبة للملاحظات المتزامنة ، قم بتعيين الوزن الأكبر للقياس الأكثر موثوقية.

Output surface type (optional)

Surface type to store the interpolation results.

· PREDICTION—Prediction surfaces are produced from the interpolated values.

· PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

· CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

13. Output surface type (optional) نوع سطح الإخراج (اختياري)

Surface type to store the interpolation results.

· PREDICTION—Prediction surfaces are produced from the interpolated values.

· PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.

· CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

نوع السطح لتخزين نتائج الاستيفاء.

• التنبؤ - يتم إنتاج أسطح التنبؤ من القيم المحرف.

• PREDICTION_STANDARD_ERROR - تنتج أسطح الأخطاء المعيارية من الأخطاء المعيارية للقيم المحرف.

• CONDITION_NUMBER - يشير سطح رقم الحالة المكانية إلى استقرار العمليات الحسابية في موقع معين. كلما زاد رقم الشرط ، زاد التوقع غير المستقر ، وبالتالي فإن المواقع التي تحتوي على أرقام كبيرة للحالات قد تكون عرضة للقطع الأثرية والقيم المتوقعة غير المنتظمة.

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