DesignMentor: A Pedagogical Tool For Computer Graphics And .

DesignMentor: A Pedagogical Tool forComputer Graphics andComputer Aided DesignJohn L. Lowther and Ching Kuang SheneProgrammers: Yuan Zhao and Yan Zhou (ver 1)Budirijanto Purnomo (ver 2)Michigan Technological UniversitySupported by the National Science Foundationunder grants DUE 9653244 and CCR 9696084

MotivationTeaching curves and surfaces is achallenging taskMajor obstacles: formidable mathematicslack of pedagogical toolsLearning curves and surfaces is alsoa difficult taskThe concepts are abstract and difficult tovisualize; without knowing the details, writingprograms to experiment is not easy; andsome concepts and algorithms are simply toodifficult to implement.There is virtually no toolsYes, there are tools. Most of them are librariesfor programming or packages (e.g., MAPLEand Mathematica). These tools are not veryhelpful for illustrating the fundamentals.So, we designed DesignMentor!

What DesignMentor Is?DesignMentor provides studentswith an interactive environment forlearning, practicing, and visualizingmost fundamental concepts andalgorithms in curves and surfacesWhat DesignMentor Is Not?DesignMentor is not a productionsystem for helping students learndesign issues and practice designskills.

Overview of DesignMentorDesignMentor supports Bezier,rational Bezier, B spline and NURBScurves and surfacesDesignMentor is portable andsupports Windows 95/98/NT, SGIand Sun platformsSystem Architecture of DesignMentorGraphical User InterfaceCross Sectional penGL/Mesa

DesignMentor’s Curve SystemA student can click on the canvas forcreating a number of control pointsand select a curve type (e.g., Bezier).DesignMentor generates the curveDesignMentor can display manyimportant geometric propertiesMoving TriadDrawing Canvas1st DerivativeCurveTracingPointControl PolygonCurvature SphereTracingSliderRoller CoasterControl Point

De Casteljau’s and de Boor’sAlgorithmsDesignMentor can display the convexhull and a step wise execution ofde Casteljau’s/de Boor’s algorithmThe computation and visualizationare updated on the fly as the curveis being tracedConvex HullComputed Pointde Boor NetComputation of de Boor’salgorithm. Can be donestep wise.

Shape EditingDesignMentor supports shape editingMoving control points: all curvesChanging weights of control points:Rational Bezier and NURBSModifying knots: B spline and NURBSShape editing is global for Bezier andrational Bezier curvesBezierbeforeafterB splinedo notchange

Modifying Weights (NURBS)Weights can also be modified forrational Bezier and NURBS curvesIncreasing (resp., decreasing) the weight ofa control point pulls (resp., pushes) the curvetoward (resp., away from) that pointA user selects a control point andchanges its weight. The effect is shownon the fly.BeforeAfterw 1w 1w 0.3NURBS curve of degree 5w 4

Advanced Geometric AlgorithmsDesignMentor supports 3 advancedalgorithms for B spline and NURBS:Knot insertion:inserting a new knotSubdivision:dividing a curve into twoDegree Elevation: increasing the degree by 1Beforeinsertionknotsnew control pointsnew knotcorners cutAfterinsertionnew knotB spline ofdegree 5

Curve InterpolationDesignMentor also supports curveinterpolation and approximationA user clicks data points on the canvas andDesignMentor constructs a B spline curvethat contains all points in the given orderUnder Global Interpolation modifying a datapoint changes the curve globally.Under Local Interpolation modifying a datapoint only affects the curve locally.Global InterpolationLocal InterpolationBezier curve of degree 3data pointsdata points

DesignMentor’s Surface SystemDesignMentor supports Bezier,rational Bezier, B spline and NURBSsurfaces.A user indicates the type of a surfaceand its degrees. DesignMentorgenerates a flat surface.Then, a user create the desired surfacewith shape editing operations.control pointtracing pointmove control pointsdomain (u,v)move to traceknotscontrol net

Surface Shape EditingTo change the shape of a surface,a user canmove control points (all surfaces)modifying knots (B spline and NURBS)change weights (rational Bezier and NURBS)A zero weight means no contributionto the creation of the surfacebefore weight changeafter weight changew 10w 1w 1w 0.1

De Casteljau’s and de Boor’sAlgorithmsDe Casteljau’s/de Boor’s algorithmfor curves can be extended to surfacesApply the algorithm to each row ofcontrol points creating a set of newpoints, followed by one application ofthe algorithm to the new points.apply the algorithmto the new pointsto get thisapply the algorithmto each rowget this new point

Advanced Geometric AlgorithmsDesignMentor supports knotinsertion, degree elevation andsurface subdivision both u and vdirections.Each subpatch is color codedv 0.5u 0.75

Cross Sectional DesignCross Sectional Design is a techniqueof surface design using a number ofcurves (i.e., profile cross section andtrajectory curves)DesignMentor supports the followingsurface types:Ruled surface: two curvesSurface of revolution: one profile curveSwung surface: one profile and onetrajectory curveSimple swept surface: one profile and onetrajectory curveSkinned surface: a number of profile curvesSwept by skinning: one trajectory and a setof (transformed) profile curvesThe surface system activates thecurve system for designing profile andtrajectory curves

Ruled SurfacesIt takes two curves for designing aruled surface.The surface is created by joiningcorresponding points on curves withline segments.first curvesecond curve (line segment)line segment

Swung SurfacesA swung surface is very similar to asurface of revolutionIn addition to an axis of revolution,a trajectory curve is requiredAs the profile curve rotates about theaxis, it is scaled by the trajectory curvetrajectory curveaxis ofrevolutionprofile curvesurface is rotated to show the detail

Skinned SurfacesA skinned surface requires a set ofprofile curvesDesignMentor constructs a B splinesurface to contain all given curvesThus, skinning is a form of inter polation (of curves)profile curves (circles)

Swept by SkinningDesignMentor can construct complexswept surfaces via skinningA master profile curve is requiredInstances of this master curve areplaced along the trajectory curveand can be rotated and scaledThen, skinning is appliedmaster profiletransformed masters

Interpolation and ApproximationDesignMentor supports global andlocal interpolation and globalapproximation for regular griddata point gridglobal interpolationcompare the resulting surfaceslocal interpolationcompare the resulting surfacesglobal approximationcompare the resulting surfaces

Curve Network InterpolationDesignMentor supports interpolationon a curve networkA user can design a curve networkwith DesignMentor or other systemThen, DesignMentor interpolatesthe curve network with a surface,the Gordon Surfacecurve networkGordon surface

Future WorkMore visualization of geometricproperties (e.g., tangent plane, normalvector, curvature sphere, umbilic,Dupin indicatrix, .)Triangular and multi sided patchesCurve and surface interrogationSubdivision schemeThe Blossoming PrincipleIrregular data interpolation andapproximation

Advanced Geometric Algorithms DesignMentor supports 3 advanced algorithms for B spline and NURBS: Knot insertion: inserting a new knot Subdivision: dividing a curve into two Degree Elevation: increasing the degree by 1 knots new knot new control points corners cut new knot Before insertion After insertion B spline of degree 5