3D freeform surfaces from planar sketches using neural networks

A novel intelligent approach into 3D freeform surface reconstruction from planar sketches is proposed. A multilayer perceptron (MLP) neural network is employed to induce 3D freeform surfaces from planar freehand curves. Planar curves were used to represent the boundaries of a freeform surface patch. The curves were varied iteratively and sampled to produce training data to train and test the neural network. The obtained results demonstrate that the network successfully learned the inverse-projection map and correctly inferred the respective surfaces from fresh curves

Realtime curve interpolators

The amount of geometric information that must be transferred between a system and a computerized numerical control system creates a conflict between part precision on the one hand and feedrate fidelity and communications load on the other. This is the motivation for the development of new curve interpolation algorithms for CNC. The interpolation depends on the method of curve representation, i.e. the use of an implicit or a parametric from. Accordingly, the paper presents two realtime interpolation algorithms and compares them with existing interpolators. With the new interpolators, the amount of geometric information transferred from the system to the CNC system is reduced by orders of magnitude. Moreover, the contour errors caused by the new interpolators are much smaller than those caused by conventional interpolators.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31229/1/0000132.pd

A New Interface for Conceptual Design Based on Object Reconstruction from a Single Freehand Sketch

are troublesome for curvature-based classification, and (b) it has a short execution time that is not dependent on the length of the stroke or the number of sample points acquired (assuming coordinates have been summed while drawing the stroke). The procedure can therefore be used to provide continuous feedback of the interpreted entity during drawing, in real time. However, in spite of this ability, it is evident that geometrical-based classification is inherently limited and a more general, context-sensitive approach must be pursued. A new endpoint clustering scheme has also been presented based on adaptive tolerances at different parts of the sketch. The proposed formulation provides a framework for implementing various criteria for determining local thresholds, such as detail sensitive criteria, dynamic criteria, or other application specific criteria. Again, clustering can be improved using a contextsensitive approach. Acknowledgments This research has been supported in part by the Fund for 4 Pavlidis, T., and Van Wyk, C. J., 1985, "An Automatic Beautifler for Drawings and Illustrations," SIGGRAPH 85, Vol. 19, No. 3, pp. 225-234. 5 Bengi, F., and Ozguc, B., 1990, "Architectural Sketch Recognition," Architectural Science Review, Vol. 33, pp. 3-16. 6 Eggli, L., BrUderlin, B. P., and Elber, G. Introduction Improperly designed engineering products may fail in fatigue causing losses in revenue and personal injury or death. Currently, these failures are avoided by either using expensive design techniques involving extensive modeling and testing or by over designing the part. The expense of testing and modification of the initial design is reduced if the design criterion gives a good initial approximation. Several design approaches have been developed to address the problem of fatigue damage of ductile metals loaded with positive mean and alternating stresses. The Bagci, Gerber, Nichihara, modified Goodman, Quadratic, and Soderberg lines are a few of the techniques that have been proposed to address the problem. This paper presents the modified Findley line for designing parts which experience positive mean stress fatigue loading. The modified Findley line is based on the assumption that the critical shear decreases with an increase in the normal stress acting on the same plane, and is simple and less conservative than the modified Goodman line. The Modified Findley Line Flavenot and Skalli (1984) stated "the mechanism corresponding to the initiation of fatigue cracks is most often the shearing of crystallographic planes. It appears logical then to have a criterion relating the normal stress to alternating shear stress which might be local shear stress in most favorable oriented plane." This assumption was used before by Stanfield (1935), who suggested that both the shear and normal stresses on the fatigue plane should be considered in a fatigue failure criterion and proposed the relation (1) where TN and ON are the shear and normal stresses components on the critical plane; /and k are materials constants. Stulen and Cummings (1954), and Findley et al. (195 6) used similar forms as fatigue criteria to address the problem of absolutely reversing fatigue. Findley (1959) used the linear relationship between shear stress and normal stress on a critical plane to include the effect of mean stress on the fatigue of metals under combined loading. Journal of Mechanical Design MARCH 1997, Vol. 119/135 Copyright © 1997 by ASME where a^^" and <7" are the maximum and alternating fatigue stresses; / and k are experimental constants. Since these constants may vary with the design parameters, including materials, the actual design must be tested to determine the values of / and k. To experimentally find the values of these constants, the life of the part is determined, and at this point the values of / and k are of only academic interest. Thus, if the fatigue criterion presented in Eq. It should be noted that the negative root of Eq. Upon the application of condition (b), Eq. (4) becomes /=A:5",. Equations Substituting Eqs. 5" -[-S" + 4SI + 4(5", -5")(S", -a") ], (10) 2(5",-5") which is called the modified Findley line. Comparison With Actual Experimental Data The modified Findley, Gerber, and modified Goodman lines were compared with the experimentally developed fatigue data found in the literature. Typical data showing the fatigue points of both ferrous and non-ferrous ductile materials are shown in As shown in these figures and comparison done by Wang (1995), the modified Findley line falls between the modified Goodman line and Gerber parabola, which is supported by Conclusion The modified Findley line is based on the assumption that the critical shear decreases with an increase in the normal stress acting on the same plane, then by using ultimate strength and endurance limit as parameters to obtain a good initial approximation. Limited fatigue data is available in the open literature, and more comparison should be made before the modified Findley line is universally adopted. However, form the references found, it appears that the modified Findley line is a strong candidate for .fatigue criterion for parts made of non-ferrous ductile materials, and is conservative for ferrous parts. For a design engineer, the modified Findley line is simple and easy to use, and represents a very promising approach for leading to reasonable starting designs involving positive mean stress fatigue. Reference