Geometric characteristics of conics in Bézier form

Derive coordinate-free expressions for geometric characteristics of conics written in Bézier form in terms of their control points and weights.

The logarithmic spiral, autoisoptic curve

In the Line of Investigation that in the department of “Technical Drawing” in the School of Agriculture Engineering of Madrid, we carry out on the study of The Technical Curves and his singularities, we demonstrate an interesting property of the Logarithmic Spiral. The demonstrated property consists of which the logarithmic spiral is a autoisoptic curve, that is to say that if from a point P anyone of the spiral tangent straight lines draw up to the previous arc, these form a constant angle α. This demonstration is novel and in addition we get to contribute a method to calculate the angle α given the equation of the spiral.

Non-degenerate developable triangular Bézier patches

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of non-degenerate developable triangular patches are provided.

Geometric characteristics of conics in Bézier form

Synthetic derivation of closed formulae of the geometric characteristic of a conic given in Bézier form in terms of its control polygon, (P; Q; R) and weights, (1; w; 1g)

A 800 kW I-V curve

This paper presents the measurement of the I-V curve of an 800 kW PV generator by means of an own-made capacitive load. Along the lines of some previous works, it is shown that an I-V curve analysis can also be applied to big PV generators and that, when measuring the operating conditions with reference modules and taking some precautions (especially regarding the operating cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

Gini coefficient, dissimilarity index and Lorenz curve for the spanish port system by type of goods

This paper shows the Gini Coefficient, the dissimilarity Index and the Lorenz Curve for the Spanish Port System by type of goods from 1960 to the year 2010 for business units: Total traffic, Liquid bulk cargo, Solid bulk cargo, General Merchandise and Container (TEUs) with the aim of carcaterizar the Spanish port systems in these periods and propose future strategies.

A 500-kW pv generator I-V curve

This paper presents the measurement of the I-V curve of a 500-kW PV generator by means of an own-made capacitive load. It is shown that I-V curve analysis can also be applied to big PV generators and that when measuring the operation conditions with reference modules and taking some precautions (especially regarding the operation cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

Comparison of Airborne Laser Scanning Methods for Estimating Forest Structure Indicators Based on Lorenz Curves

The purpose of this study was to compare a number of state-of-the-art methods in airborne laser scan- ning (ALS) remote sensing with regards to their capacity to describe tree size inequality and other indi- cators related to forest structure. The indicators chosen were based on the analysis of the Lorenz curve: Gini coefficient ( GC ), Lorenz asymmetry ( LA ), the proportions of basal area ( BALM ) and stem density ( NSLM ) stocked above the mean quadratic diameter. Each method belonged to one of these estimation strategies: (A) estimating indicators directly; (B) estimating the whole Lorenz curve; or (C) estimating a complete tree list. Across these strategies, the most popular statistical methods for area-based approach (ABA) were used: regression, random forest (RF), and nearest neighbour imputation. The latter included distance metrics based on either RF (NN–RF) or most similar neighbour (MSN). In the case of tree list esti- mation, methods based on individual tree detection (ITD) and semi-ITD, both combined with MSN impu- tation, were also studied. The most accurate method was direct estimation by best subset regression, which obtained the lowest cross-validated coefficients of variation of their root mean squared error CV(RMSE) for most indicators: GC (16.80%), LA (8.76%), BALM (8.80%) and NSLM (14.60%). Similar figures [CV(RMSE) 16.09%, 10.49%, 10.93% and 14.07%, respectively] were obtained by MSN imputation of tree lists by ABA, a method that also showed a number of additional advantages, such as better distributing the residual variance along the predictive range. In light of our results, ITD approaches may be clearly inferior to ABA with regards to describing the structural properties related to tree size inequality in for- ested areas.