The QtiPlot Handbook
PrevChapter 6. Analysis of data and curvesNext

Surface Fitting

QtiPlot includes quick access to the following built-in 2D functions z = f(x, y) that can be used for surface fitting:

Table 6-2. Built-in 2D fit functions in QtiPlot.

Exponential2DGauss2DLogisticCumLorentz2DParabola2D
PlanePoly2DPolynomial2DPower2DVoigt2D

Exponential2D

This function is used to fit an exponential surface: z = z0 + Be-x/C - y/D, where z0 is the offset along the Z axis, B is the height, C is the width across the X axis and D the width across the Y axis. This function depends on a total number of 4 parameters.

Figure 6-14. The Exponential2D function with z0 = 0, B = 1, C = 2 and D = 2.

Gauss2D

This function is used to fit a Gaussian surface: z = z0 + Aexp{-1/2[(x - xC)/w1]2 - 1/2[(y - yC)/w2]2} , where z0 is the offset along the Z axis, A is the height, xC is the X center, w1 is the width across the X axis, yC is the Y center and w2 is the width across the Y axis. This function depends on a total number of 6 parameters.

Figure 6-15. The Gauss2D function with z0 = 1, A = 11, xC = yC = 0 and w1 = w2 = 3.

LogisticCum

This is the logistic cumulative function: z = z0 + B/{[1 + e(C - x)/D][1 + e(E - y)/F]} , where z0 is the offset along the Z axis, B is the height, C is the X offset, D is the width across the X axis, E is the Y offset and F is the width across the Y axis. This function depends on a total number of 6 parameters.

Figure 6-16. The LogisticCum function with z0 = 0, B = 1, C = 1, D = 2, E = 1 and F = 2.

Lorentz2D

This function is defined as: z = z0 + A/{[1 + ((x - xc)/w1)2][1 + ((y - yc)/w2]2)} , where z0 is the offset along the Z axis, A is the height, xc is the X center, w1 is the width across the X axis, yc is the Y center and w2 is the width across the Y axis. This function depends on a total number of 6 parameters.

Figure 6-17. The Lorentz2D function with z0 = 1, A = 11, xc = yc = 0 and w1 = w2 = 3.

Parabola2D

This function is used to fit a parabolic surface: z = z0 + ax + by + cx2 + dy2, where z0 is the offset along the Z axis. It depends on a total number of 5 parameters.

Figure 6-18. A 2D parabola with z0 = 0, a = 1, b = 1, c = 2 and d = 2.

Plane

This function is used to fit a planar surface: z = z0 + ax + by, where z0 is the offset along the Z axis, a is the slope in the X coordinate and b is the slope in the Y coordinate.

Figure 6-19. A plane surface with z0 = 1, a = 1 and b = 1.

Poly2D

The function used is: z = z0 + ax + by + cx2 + dy2 + fxy, where z0 is the offset along the Z axis. It depends on a total number of 6 parameters.

Figure 6-20. The Poly2D function with z0 = 0, a = 1, b = 1, c = 3, d = 3 and f = 2.

Polynomial2D

This is the X-Y polynomial function: z = z0 + A1x + B1y + A2x2 + B2y2 + ... + Anxn + Bnyn, where n is the order of the polynomial and z0 is the offset along the Z axis. If n = 1 this function is identical to the plane function.

Figure 6-21. The cubic Polynomial2D function (n = 3) for z0 = A1 = A2 = A3 = B1 = B2 = B3 = 1.

Power2D

This is the non-linear power function: z = z0 + BxC + DyE + FxCyE, where z0 is the offset along the Z axis. It depends on a total number of 6 parameters.

Figure 6-22. The Power2D function with z0 = 0, B = 1, C = 2, D = 1, E = 3 and F = 1.

Voigt2D

This function is defined as: z = z0 + A{μ/[(1 + ((x - xc)/w1)2)(1 + ((y - yc)/w2)2)] + (1 - μ)*exp[-1/2((x - xC)/w1)2 - 1/2((y - yC)/w2)2]} , where z0 is the offset along the Z axis, A is the height, xc is the X center, w1 is the width across the X axis, yc is the Y center, w2 is the width across the Y axis and μ is the profile shape factor. This function depends on a total number of 7 parameters.

Figure 6-23. The Voigt2D function with z0 = 1, A = 11, xc = yc = 0, w1 = w2 = 3 and μ = 0.4.

PrevHomeNext
Built-in fit functionsUpUser defined fit models