gridding rules for points
[surfit gridding rules]


Functions

bool surfit::points (const char *points_name_or_position="0")
bool surfit::points_add (REAL weight=1, const char *points_name_or_position="0")
bool surfit::points_leq (const char *points_name_or_position="0", REAL mult=REAL(0.001))
bool surfit::points_geq (const char *points_name_or_position="0", REAL mult=REAL(0.001))

Function Documentation

bool points (  const char *  points_name_or_position = "0"  ) 
 

Tcl syntax:
points "points_name_or_position"
Description:
Using this rule the resulting surface approximates points in least squares meaning. If each cell contains no more than one point, resulting surface interpolates points.
Parameters:
points_name_or_position name of points dataset, or points position number.
Math:
This command adds the following functional to the functional sequence:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z_p \right)^2, \]

where points with coordinates $ (x_p, y_p) $ are belong to the cells (i,j)

Examples:
area_completer.tcl, canyon_map.tcl, fault.tcl, fault_aniso.tcl, ineq.tcl, map_hor_frac.tcl, map_ver_frac.tcl, mask_completer.tcl, mask_mean.tcl, mask_surf_ineq.tcl, mask_wmean.tcl, mean.tcl, points.tcl, points_exact.tcl, surface_ineq.tcl, trend.tcl, and wmean.tcl.

bool points_add (  REAL  weight = 1,
const char *  points_name_or_position = "0"
) 
 

Tcl syntax:
points_add weight "points_name_or_position"
Description:
This function modifies previous (modifiable) rule by adding the points rule with some weight.
Parameters:
weight informational weight for this rule
points_name_or_position name of points dataset, or points position number.
Math:
This command modifies previous functional $ \Phi_0 $ by adding $ \Phi_1 $:

\[ \Phi(u_{1,1},\ldots,u_{N,M}) = \Phi_0(u_{1,1},\ldots,u_{N,M}) + w\Phi_1(u_{1,1},\ldots,u_{N,M}), \]

where $ w $ - informational weight,

\[ \Phi_1(u_{1,1},\ldots,u_{N,M}) = \sum_{p=1}^P \left( u_{i,j} - z_p \right)^2, \]

where points with coordinates $ (x_p, y_p) $ are belong to the cells (i,j)

Examples:
fault_approx.tcl, flow_points2.tcl, and points_approx.tcl.

bool points_geq (  const char *  points_name_or_position = "0",
REAL  mult = REAL(0.001)
) 
 

Tcl syntax:
points_geq "points_name_or_position" mult
Description:
This rule adds the surface condition - "the surface should be greater than equal to points". In case of the penalty algorithm algorithm bad convergence or unexpected (wrong) result, you should carefully review your conditions and if they are correct, try to change "mult" parameter
Parameters:
points_name_or_position name of points dataset, or points position number.
mult multiplier parameter for penalty algorithm algorithm
Math:
This command adds the condition:

\[ u_{i,j} \geq z_p, \quad p=1,\ldots,P \]

where points with coordinates $ (x_p, y_p) $ are belong to the cells (i,j)

Examples:
points_ineq.tcl.

bool points_leq (  const char *  points_name_or_position = "0",
REAL  mult = REAL(0.001)
) 
 

Tcl syntax:
points "points_name_or_position" mult
Description:
This rule adds the surface condition - "the surface should be lower than equal to points". In case of the penalty algorithm algorithm bad convergence or unexpected (wrong) result, you should carefully review your conditions and if they are correct, try to change "mult" parameter
Parameters:
points_name_or_position name of points dataset, or points position number.
mult multiplier parameter for penalty algorithm algorithm
Math:
This command adds the condition:

\[ u_{i,j} \leq z_p, \quad p=1,\ldots,P \]

where points with coordinates $ (x_p, y_p) $ are belong to the cells (i,j)

Examples:
points_ineq.tcl.


surfit: open source gridding and contouring software.