Research article

Comparison of selected splines for stem form modeling: A case study in Norway spruce

Karel Kuželka , Róbert Marušák

Karel Kuželka
Department of Forest Management, Faculty of Forestry and Wood Sciences, University of Life Sciences in Prague. Kamýcká 1176; 165 21 Praha 6 – Suchdol, Czech Republic. Email: kuzelka@fld.czu.cz
Róbert Marušák
Department of Forest Management, Faculty of Forestry and Wood Sciences, University of Life Sciences in Prague. Kamýcká 1176; 165 21 Praha 6 – Suchdol, Czech Republic

Online First: April 11, 2014
Kuželka, K., Marušák, R. 2014. Comparison of selected splines for stem form modeling: A case study in Norway spruce. Annals of Forest Research DOI:10.15287/afr.2014.177


Natural cubic spline has been frequently used to represent stem forms, with other spline types rarely involved. Splines are a large class of functions and there are many other spline types which might serve that purpose. In this paper several different spline types, both interpolation and approximation, were investigated and splines more suitable for stem form representation than natural cubic spline are proposed. Their abilities to model the stem curve using different numbers of input points were compared using data of 85 carefully measured Norway spruce (Picea abies [L.] Karst.) stems. When modeling the whole stem profile all interpolation curves with second degree continuity suffer from oscillations. Approximation splines give satisfactory overall estimations, but they overestimate the lower stem and overestimate the upper stem. The best results were obtained with interpolation curves with first degree continuity. Stem curves were best described by the Catmull-Rom spline. Previously frequently used natural cubic spline performed worse than number of other splines.


Biging G.S., 1984. Taper equations for second-growth mixed conifers ofNorthern California.ForestScience 30: 1103–1117.

ClarkN.A., Wynne R.H., Schmoldt D.L., Winn M., 2000. An assessment of the utility of a non-metric digital camera for measuring standing trees. Computers and Electronics in Agriculture 28: 151-169. DOI: 10.1016/S0168-1699(00)00125-3.

Dean C., 2003. Calculation of wood volume and stem taper using terrestrial single-image close-range photogrammetry and contemporary software tools. Silva Fennica 3: 359-380.

Demaerschalk J.P., 1972. Converting volume equations to compatible taper equations.ForestScience 18: 241–245.

Figueiredo-Filho A., Borders B.E., Hitch K.L., 1996. Number of diameters required to represent stem profiles using interpolated cubic splines. Canadian Journal of ForestResearch 26: 1113–112. DOI: 10.1139/x26-124.

Flewelling J.W., Raynes L.M., 1993. Variable-shape stem-profile predictions for western hemlock. PartI.Predictions from DBH and total height. Canadian Journal of ForestResearch 23: 520–536. DOI: 10.1139/x93-070.

Hapca A.I., Mothe F., Leban J.-M., 2007. Adigital photographic method for 3D reconstruction of standing tree shape. Annals of ForestScience 64: 631-637. DOI: 10.1051/forest:2007041.

Goulding C.J., Murray J.C., 1976. Polynomial taper equations that are compatible with tree volume equations.New ZealandJournal of Forestry Science 5: 313–322.

Goulding C.J., 1979. Cubic spline curves and calculation of volume of sectionaly measured trees.New ZealandJournal of Forestry Science 9: 89–99.

Jiang L., Brooks J.R., Wang J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. ForestEcology and Management 213: 399–409. DOI: 10.1016/j.foreco.2005.04.006.

Kochanek D.H.U, Bartels R.H., 1984. Interpolating splines with local tension, continuity, and bias control. SIGGRAPH Computer Graphics 18: 33–41. DOI: 10.1145/964965.808575.

Koskela L., Nummi T., Wenzel S., Kivinen V.-P., 2006. On the analysis of cubic smoothing spline-based stem curve prediction for forest harvesters. Canadian Journal of ForestResearch 36: 2909–2919. DOI: 10.1139/x06-165.

Lahtinen A., 1988. On the construction of monotony preserving taper curves. Acta Forestalia Fennica 203: 1–34.

Laasasenaho J., Melkas T., Aldén S., 2005. Modelling bark thickness of Picea abies with taper curves. ForestEcology and Management 206: 35–47. DOI: 10.1016/j.foreco.2004.10.058.

Lin H., Wang G., Dong C., 2004. Constructing iterative non-uniform B-spline curve and surface to fit data points. Science in ChinaSeries F 47: 315–331. DOI: 10.1360/02yf0529.

LinkeováI., 2007. NURBS křivky. NeUniformní Racionální B-Spline křivky. [NURBS curves. Non-Uniform Rational B-spline curves.] Nakladatelství ČVUT. Praha, 208 p.

Lee W.-K., Seo J.-H., Sonm Y.-M., Lee K.-H., von Gadow K., 2003. Modeling stem profiles for Pinus densiflora in Korea. ForestEcology and Management 172: 69–77. DOI: 10.1016/S0378-1127(02)00139-1.

Liu C.J., 1980. Log volume estimation with spline approximation. Forest Science 26: 361–369.

Lovell J.L., Jupp D.L.B., Newnham G.J., Culvenor D.S., 2011. Measuring tree stem diameters using intensity profiles from ground-based scanning lidar from a fixed viewpoint. ISPRS Jounal of Photogrammetry and Remote Sensing 66: 46-55. DOI: 10.1016/j. isprsjprs.2010.08.006.

MacCalum K.J., Zhang J.-M., 1986. Curve-smoothing techniques using B-splines. The Computer Journal 29: 564-571.DOI: 10.1093/ comjnl/29.6.564.

The MathWorks, Inc. MATLAB and Statistics Toolbox Release 2012b,Nattick,Massachusetts,United States.

Max T.A., Burkhart H.E., 1976. Segmented polynomial regression applied to taper equations.ForestScience, 22: 283–289.

Pfeifer N., Winterhalder D., 2004. Modelling of tree cross sections from terrestrial laser scanning data with free-form curves. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 8-W2: 76-81.

Piegl L., Tiller W. 1996. The NURBS Book, 2nd ed. Springer-Verlag. Berlin, 646 p.

Rojo A., Perales X., Sánchez-Rodríguez F., Álvarez-González J.G., von Gadow K., 2005. Stem taper functions for maritime pine (Pinus pinaster Ait.) in Galicia(Northwestern Spain). European Journal of Forest Research 124: 177-186. DOI: 10.1007/s10342-005-0066-6.

Smaltschinski T., 1983. Individuelle Baumschaftform und cubische Spline Interpolation. [Indivudual taper curve of trees and cubic spline interpolation]. Allgemeine Forst- und Jagdzeitung 155: 193–197.

Thomas C.E., Parresol B.R., 1991. Simple, flexible, trigonometric taper equations. Canadian Journal of ForestResearch 21: 1132–1137. DOI: 10.1139/x91-157.


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