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WO2001008102A1 - Systeme de conception et de modelisation geometriques utilisant une geometrie de controle - Google Patents

Systeme de conception et de modelisation geometriques utilisant une geometrie de controle Download PDF

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Publication number
WO2001008102A1
WO2001008102A1 PCT/US1999/016844 US9916844W WO0108102A1 WO 2001008102 A1 WO2001008102 A1 WO 2001008102A1 US 9916844 W US9916844 W US 9916844W WO 0108102 A1 WO0108102 A1 WO 0108102A1
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WIPO (PCT)
Prior art keywords
profile
points
geometric object
curve
geometric
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/US1999/016844
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English (en)
Inventor
John N. Lee
Alyn Rockwood
Lance Hagen
Scott Hagen
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Curventa Softworks LLC
Original Assignee
Curventa Softworks LLC
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority to AU53907/99A priority Critical patent/AU5390799A/en
Priority to MXPA02000845A priority patent/MXPA02000845A/es
Priority to HU0700118A priority patent/HUP0700118A2/hu
Priority to EP99939655A priority patent/EP1210692A4/fr
Priority to CA002379459A priority patent/CA2379459A1/fr
Priority to JP2001513115A priority patent/JP2003505800A/ja
Application filed by Curventa Softworks LLC filed Critical Curventa Softworks LLC
Priority to CN99816901A priority patent/CN1391683A/zh
Priority to PCT/US1999/016844 priority patent/WO2001008102A1/fr
Publication of WO2001008102A1 publication Critical patent/WO2001008102A1/fr
Priority to KR1020020004000A priority patent/KR20020021800A/ko
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T13/00—Animation
    • G06T13/20—3D [Three Dimensional] animation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/30—Polynomial surface description
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T19/00—Manipulating 3D models or images for computer graphics
    • G06T19/20—Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts

Definitions

  • the present invention relates to a system and method for performing computer aided design, and, in particular, to
  • CAD computer aided design
  • geometric object (such as a surface) by first specifying prominent and/or necessary subportions of the geometric object through
  • such subportions may be points, curves, surfaces and/or higher
  • a designer that designs a surface may construct and position a plurality of curves
  • the intended surface is, in general, expected to have geometric characteristics (such as differentiability and curvature) that,
  • an intended exterior surface of a bottle may
  • subportions such as: (a) feature curves positioned in high curvature portions of the bottle surface, and
  • the intention of a bottle surface designer is to construct a bottle design that satisfies his/her input
  • the designer may desire to generate holes for handles, as well as, e.g., ergonomic
  • the designer/user may encounter lengthy delays due to substantial computational overhead and/or the designer/user may
  • control points By defining and/or manipulating designated points denoted as "control points.” However, such techniques can be computationally
  • control vectors That is, the direction of these vectors may be used to define the shape or contour of an associated
  • each of the control vectors typically corresponds to only a single point of the surface isolated from other surface points having
  • two geometric objects intended to abut one another along a common boundary may not be within a
  • boundary may not be considered “water tight,” which may be problematic in certain machining operations and other
  • a "parametric geometric object'1 is a geometric object that is the image of a function f , wherein the domain
  • S will be a geometrically simpler object than its image in object space.
  • space may be a simple line segment 172, L, in parameter space.
  • S denotes the curve in object space, then notationally f
  • a “profile” ⁇ (Fig. 16) is a geometric object, such as a curve in object space, through which an associated object
  • profiles provide a common and natural way for artists and designers to geometrically design objects, in
  • profile curves on a surface may substantially define the geometry of a resulting
  • a profile may,
  • fractal contours may be in some measure imparted to the surface of the derived geometric object adjacent the profile. Further note that it is within the scope of the present
  • a profile may also be a surface or a solid. Accordingly, if
  • a profile is a surface, then a solid having locally (i.e., adjacent to the profile) at least some of the geometric characteristics of
  • the profile may be derived.
  • profiles may have various computational representations such as linear (e.g.,
  • interpolation for deforming or reshaping each profile is preferable. More particularly, it may be preferable that such a method
  • predetermined points being continuous, being differentiable, having a minimal curvature, etc. Further, note that such a
  • deformation method may also include the ability to decompose a profile into subprofiles, wherein the common boundary (e.g.,
  • a point) between the subprofiles may be "slidable" along the extent of the original profile.
  • a “marker'l ⁇ Z (Fig. 16) is a point on a profile that can be moved to change the shape of the profile 200 in a region
  • a marker also designates a position on a profile where the shape of a geometric object having the profile
  • a “profile handle”l ⁇ 2 (Fig.16) is a geometric object tangent to the profile 200. Such a profile handle may control
  • a profile handle may be used to control the general shape of the profile by indicating a trend direction and
  • the profile is a fractal or other nondifferentiable geometric object
  • a profile handle may, for example, provide a range within the object space to which the profile must be confined; i.e., the range
  • the profile may be of a tubular configuration wherein the profile is confined to the interior of the tubular configuration, Note that the profile
  • handle 212 affects the fullness of the profile 200 (e.g., the degree of convexity deviating from a straight line between markers on
  • An "isocline boundary" ⁇ Uft is the boundary curve opposite the profile 200 on the isocline ribbon 216.
  • each point on the profile 200 there is a paired corresponding point on the isocline boundary 200, wherein each
  • such pair of points defines a vector 224 (denoted a "picket") that is typically transverse to a tangent vector at the point on
  • the isocline boundary 220 can be viewed as a collection of pickets at
  • An "isocline ribbon or simply isocline) is a geometric object, such as a surface 216, which defines the slope of
  • ribbon may be considered as the representation of a geometric object delimited by the profile 200, the isocline handles 218a and
  • I O isocline ribbon 216 along the profile 200. Said another way, in one embodiment, the geometric object 204 must be continuous
  • object 204 may be constrained by the isocline 216 so that the object 204 lies within a particular geometric range in a similar
  • each profile 200 is a boundary for two abutting surfaces (e.g. two abutting surfaces 204).
  • An "isocline handlell is a geometric object (e.g., a vector) for controlling the shape of the isocline ribbon 216
  • profile handle and isocline handle at the marker may define a plane tangent to the surface 204.
  • isocline handle is used to determine the shape of the surface 204 (or other underlying geometric object) about the
  • an isocline handle 228 is a user manipulatible picket 224. If all the profile handles 212 and isocline
  • handles 228 e.g., for two or more abutting surfaces
  • handles 228 are coplanar at a marker 208, then the surface 204 will be smooth at the
  • the part of the profile 200 between two markers 208 is denoted a "profile segment”!!!. Similarly, the part of
  • isocline ribbon 216 between two isocline handles 228 is denoted a ribbon segment! ⁇ .
  • a "boundary segment"! ⁇ denotes the part of the boundary 220 between two isocline handles 228.
  • the vector 246 that is the derivative tangent to the isocline boundary 220 at an isocline handle 228 is denoted a
  • ribbon tangent Note that modifications of ribbon tangents can also be used by the present invention to control and/or
  • Isocline handles 228 may be generalized to also specify curvature of the surface 204. That is, instead of straight vectors
  • the handles may be curved and denoted as "isocline ribslt ⁇ .
  • isocline ribslt ⁇ may facilitate preserving
  • ribbons are composed of isocline ribs. Accordingly, the curvature of such surfaces will match the curvature of their corresponding
  • isocline ribs in much the same way as they match in tangency.
  • a "developable surface” is a surface that can be conceptually rolled out flat without tearing or kinking is
  • the surface perpendiculars are all equal in direction along the ruling.
  • Label surfaces ditnoti special 2-dimensional (developable or nearly developable) surfaces wherein a label may
  • Label surfaces allow application of a decal without tearing or creasing. These surfaces are highly
  • a "trim profile' ' is a geometric object (curve) that is a profile for trimming another geometric object (e.g., a
  • the trim profile may have a single corresponding isocline ribbon 216 since if the surface to be trimmed is a label surface,
  • a trim profile can be used to delimit any surface, not just a label surface.
  • a surface, S that is blended along
  • a trim profile with one or more other surfaces is called an "overbuilt surface" when the surface S overhangs the trim profile.
  • surface 130 is an overbuilt surface, wherein the portion of the surface outside of the area 134 is typically
  • a convex combination of arguments F is a summation ⁇ c F ⁇ where the c, are scalar coefficients and
  • scalar multiplication is well-defined for the F, (e.g., F, being vectors, functions, or differential operators), and where c, ⁇ 0 and
  • a "forward evaluation” is a geometric object evaluation technique, wherein in order to generate a set of sample
  • parametric path on a parametrically defined geometric object are continuous, e.g., tangent vector magnitudes are not considered.
  • the present invention is a computational geometric design system that is capable of sufficiently efficient computations
  • present invention is a paradigm shift away from typical CAD systems since, in a typical CAD system the user must supply input
  • updates may be processed in real-time immediately upon input receipt without the user explicitly indicating
  • a user of the present invention can more
  • portions of such objects may be satisfactorily designed with a wide range of geometric characteristics.
  • the CAD system of the present invention enables novel design techniques by providing a novel computational technique
  • each surface S, and S 2 has a respective blending function B,(u,v) and B 2 (u,v) such that each of the blending functions has, for example, (0,1 ) as its range for u and v (as well as satisfying other properties given hereinbelow),
  • a new surface, S may be defined by the following formula:
  • blending functions B, and B 2 are typically chosen so that the resulting blended surface S is the same as S, on a
  • the present invention may be used for blending between a plurality of geometric objects
  • blending functions B, and B 2 may also be defined for such other parameter spaces. Additionally, it is worthwhile to note that such
  • blending functions B, and B 2 may be considered as weights of a weighted sum of points selected from the surfaces (more generally,
  • weight/blending function B may be provided for each value of i so that the following variation of Formula (I) is obtained:
  • S 2 are parameterized solids, then S may be generated as a solid blended from S, and S 2 using another variation of Formula (I),
  • S may extend between S, and S 2 so that a surface P, of S, and a surface P 2 of S 2
  • S is represented as a weighted sum of points of S, and S 2 similar to Formula (I).
  • one or more of the parametric geometric objects S, of Formula (I) (or
  • the present invention that the underlying geometric objects that define the S,'s (e.g., for the S, being isocline ribbons, such
  • control points and/or geometric entities derived
  • the surface S can be deformed by changing geometric characteristics of the isocline ribbons S,.
  • curvature tangent vectors, and/or tangent planes
  • curvature may be determined by the shape of the isocline ribbons S,. More
  • the shape of the blended surface S may be changed by any user interaction technique that: (a)
  • t wherein such changes may include: changing a shape of
  • shape denotes a plurality of geometric characteristics such as continuity, differentiability, curvature, and higher order
  • S may be deformed by changing a shape of one or more of the solids S, used in determining S.
  • geometric objects S used to generate a blended geometric
  • object S may be such that the S,'s can be modified indirectly via other geometric objects from which the S,'s may be themselves
  • S is a surface blended from isocline ribbons S, and S 2 (having corresponding profiles P, and P 2 ,
  • the present invention provides user interaction techniques for modifying such handles and/or ribbon tangents
  • a user's design intent may be immediately displayed while the user is inputting such changes. Accordingly, using
  • features and/or subgeometry of a geometric object O 0 are capable of being constrained to lie within another geometric object, 0,, so that as 0, is deformed, the features and/or
  • 0, may be a curve, surface, volume or solid. Thus, as 0, is deformed, 0 alternately deforms. Moreover, instead of a point p, other
  • geometric subobjects may also be similarly constrained, such as curves, surfaces or solids. Additionally, features of a geometric
  • object 0 0 such as control points, handles (of various types, e.g., profile and isocline), normals, twist vectors, etc. may also be
  • geometric object 0 0 can be efficiently regenerated (e.g., reinterpolated) substantially in real-time when constrained features
  • invention provides for the combining of various geometric objects hierarchically so that geometric deformation control of a parent
  • structures of the geometric object embedded therein provides for the deformation of the geometric object when the three-
  • dimensional deformation space is deformed. Further, if one or more such deformation spaces are, in turn, made dependent upon a simpler geometry such as a surface or curve, then substantial control over the shape of the geometric object, however complex,
  • Fig. I shows a surface 62 generated according to the present invention, wherein the surface interpolates between the
  • Fig. 2 shows a further modification of the surfaces of Fig. I, wherein the surface 30 has a circular disk 66 blended
  • Fig. 3 shows a blended surface 62a generated according to the present invention between the surfaces 30 and 34
  • Fig.4 illustrates a correspondence between geometric entities in parameter space and geometric entities in object space
  • lines 78a and 78b of parameter space have object space images of curve 54 and 58, respectively, and additionally,
  • parameter space line 86 has as an object space image curve 80;
  • Fig.5 provides a graphical representation of two blending functions, B, and B 2 , utilized in some embodiments of the
  • Figs.6A-6D show graphs of additional blending functions that may be used with the present invention.
  • Fig.7 provides a further illustration of the correspondences between geometric entities in parameter space and object
  • Fig.8 shows an elliptic region 100 that is blended into a cylinder 108 according to the present invention, wherein the
  • closed curve 110 delimits the elliptic region from the deformed portion of the cylinder 108 that blends to the closed curve
  • Fig.9 shows a simple boss 112 created on a cylinder 116 according to the method of the present invention
  • Fig. 10 shows a composite curve 120 (as defined hereinbelow) that includes two crossing subcurves 124 and 128;
  • Fig. 11 shows a surface 130 from which a label surface 134 is trimmed
  • Fig. 12 illustrates one computational technique for determining a distance-like measurement from a point p that is
  • Fig. 13 shows two boundary curves 156a and 156b in parameter space (i.e., the unit square), wherein area patches 168
  • Fig. 14 illustrates a region that has sides and ribbons defined by three surfaces S exert S 2 and S,, wherein the present
  • invention is able to provide a surface patch for the region 300 using Formula (5) provided hereinbelow;
  • Figs. IS and 16 illustrate both general computational geometry concepts, as well as novel concepts that are fundamental
  • Fig. 17 shows a block diagram of the typical flow of design construction operations performed by a user of the present
  • Fig. 18 shows three profile curves 404, 408 and 412 meeting at a profile marker 420, wherein the surfaces 416 and 418
  • Fig. 19 shows profile curves x and y that define a surface 480 which forms a fillet between surfaces 484 and 486.
  • profiles x and y are defined using distances 488 and 490 from the intersection curve 482 of surfaces 484 and 486;
  • Fig.20 illustrates one embodiment for computing a blended surface from isocline ribbons 508 and 516 according to
  • Figs.2IA - 2IC illustrate a procedure for creating a hole 600 according to the present invention
  • Fig.22 shows a blended surface 710 according to the present invention, wherein the blended surface extends between
  • Fig.23 shows a blended surface 750 according to the present invention that extends between the degenerate profile
  • Fig.24 illustrates the results of a blending technique of the present invention for blending a surface between semi ⁇
  • Fig.25 shows a blended surface 808 according to the present invention whose points p(u,v) are determined using a
  • Fig.26 is a flowchart showing the steps for computing an interpolating curve according to the present invention using
  • Fig.27 shows a flowchart of the steps performed when constructing an approximation to an isocline boundary of an
  • isocline ribbon wherein the boundary is opposite the profile for the isocline ribbon
  • Figs.28A and 28B show a flowchart for a program that constructs a more precise isocline ribbon boundary than the
  • Figs.29A - 29C illustrate a flowchart for modifying one or more subsurfaces S,of a composite surface Snd by changing
  • Figs.30A and 30B provide a flowchart of a program invoked by the flowchart of Figs. 29 for deforming subsurfaces
  • Fig. 31 is a flowchart of the high level steps performed by a user interacting with an embodiment of the present
  • Fig. 32 pictorially illustrates examples of values for parameters used in the flowchart of Fig. 26 for computing an
  • Fig. 33 shows four profile curves P M , P l2 , P 2I and P 22 wherein it is desired to generate a surface, bounded by these
  • Figs.34 and 35 illustrate the intermediary surfaces generated during the performance of one method for creating a
  • Fig.36 shows a resulting blended surface S derived from S, (shown in Fig.34), and S 2 (shown in Fig.35), wherein S
  • Fig.37 shows the geometric objects used in an embodiment of the present invention for generating a surface S from
  • Fig.38 illustrates one embodiment of the present invention for generating a four-sided patch
  • Fig. 39 illustrates an alternative embodiment of the present invention for generating the four-sided patch also
  • Fig.40 shows the notational correspondences between the geometric objects of Fig.38 and those of Fig. 39;
  • Fig.41 shows a possible geometric configuration of Fig.38, wherein the profiles P 3 and P 4 of Fig. 38 are degenerate; Figs.42A and 42B illustrate the movement of a marker 2002 that is constrained to reside on the profiles curves 2003
  • Fig.43 illustrates constraints on composed profile curves and their corresponding isocline ribbons for providing tangent
  • Fig.44 shows a profile P, associated isocline ribbons RL and RR, and various handles used in describing the conditions
  • Fig. I illustrates the use of an embodiment of the present invention for designing a surface 62 that interpolates any
  • curve 60 are derived from (e.g., identical to) the isocline ribbons 61 and 63.
  • a designer can design a surface specified in terms of: (a) a relatively small number of carefully
  • the present invention can be used to blend a surface region into an object being designed.
  • a surface region into an object being designed.
  • Fig.2 illustrates the blending of a circular disk 66 into the cylindrical surface 30.
  • the present invention can also be
  • At least one embodiment of the present invention differs from traditional approaches to computer-aided design (CAD)
  • a desired geometric object e.g., a surface
  • a desired geometric object e.g., a surface
  • a fundamental geometric object design technique of the present invention is the blending between two parametric
  • geometric objects such as surfaces and, more particularly, the manner in which such blending is performed.
  • geometric objects such as surfaces and, more particularly, the manner in which such blending is performed.
  • a "parametric geometric object” e.g. a surface
  • a mapping may be defined as a result of a mapping
  • v) may by way of example be used to uniquely identify each point in the parameter space.
  • a function may associate a point (x,y,z) in the object
  • each surface S, and S 2 has associated therewith a respective blending function
  • each of the blending functions has, for example, (0,1) as its range (as well as satisfying other
  • blending functions B, and B 2 are typically chosen so that the resulting blended surface S is the same as S, on a
  • the surface 62a is S, which runs between these two boundaries and is tangent to S, and S 2 at the boundaries.
  • Blending functions may be provided for blending between geometric objects of various types. For example, blending
  • the point (u,v) is to the boundary curves (e.g., boundary curves 78a and 78b) and, more generally, to the pre-images of profile
  • a good collection of blending functions B not only allows the mapping, S, of a blended surface to be coincident with
  • the desired perimeter (profile) curves, but will do so in a manner so that the resulting blended surface between two or more such
  • perimeter curves of, e.g. for example, different initial surfaces will preserve such characteristics as the continuity of curvature
  • the blended surface "heels" to each of the initial surfaces. Also, it is preferred that the
  • One useful embodiment is:
  • B,(x) and B 2 (x) are polynomials satisfying the following constraints:
  • B 2 (x) l-B,(x). Note that B,(x) may be derived as a Bezier curve with six control points, P,,...,P 6 , as shown in Fig. 6D.
  • composition of blending functions as described hereinabove with a bijective e.g., one-to-one and onto
  • parameterization function P:[0,l] ⁇ [0,l] may be composed with a blending function to obtain another
  • blending functions may, in one embodiment, be tabulated prior to a design session at a sufficiently high resolution and stored
  • D,(p) is a distance-like measurement to the pre-image of the i* edge e, in the common parameter space;
  • Formula ( I ) is applied to the surfaces of Fig.35, wherein S, and S 2 of Formula ( I) are replaced by R 2I and
  • 35) may be:
  • D 2 (P 2 ) mm (D(P 2 ,P 2
  • the two surfaces S, and S 2 can be blended together using Formula (2) to obtain surface S of Fig.36.
  • All handles are piecewise linear segments
  • h L , h R the left and right hand profile handles, respectively, of the profile, P;
  • s L , s R the left and right hand isocline handles, respectively, of the profile, P; b L , b R : the left and right hand ribbon tangents at the respective left and right end points of isocline boundary R (these
  • surfaces S L and S R may be defined, wherein S L is bounded by the line segments
  • S L and S R are known in the art as "twisted flats," and accordingly, S L is denoted as the left
  • the u parameter is also the distance measure needed for B, and B 2 of Formulas (3.1).
  • v 0,
  • R is a translation of P, and such similarities may simplify the data storage
  • N-side patch parameter space (in s and t) to the parameter space of the ribbons S, (in u and v).
  • ribbon is a special case of Formula (5.03).
  • the denominator is I
  • the distance measure is just
  • these ribbons may be used to generate a four-sided patch.
  • P 3 is a blend (e.g., using Formula (I)) of h. R and h L , wherein h R is S 1 and h L is S 2
  • P 4 is a blend of h R and h L .
  • blended surface, S, of Fig.38 has tensor product form. This can be shown by decomposing Formula (5.04)
  • each of the ribbons S, and S 2 is derived from the Formula (5.01a) and (5.01b). That is, S, is a blend
  • the two-sided patch of Formula (5.04) provides a very versatile four-sided patch. Moreover, its evaluation
  • a scaling function such as
  • the so-called "boss” feature may be obtained from a blending between two profile edges.
  • the profiles may be provided
  • blending may be performed by using a neighborhood about each boundary curve
  • curves 90, 54, 58 and 91 these having respective pre-images 78a, 78b, 78c and 78d.
  • profile 78b is the pre-image of the profile 54.
  • such a profile curve, C may typically have a parametric pre-image in a parameter space, i.e.
  • curves having the following forms: (a) conies including lines, parabolas, circles and ellipses; Bezier, Hermite and non-
  • NURBS uniform rational b-splines
  • b trigonometric and exponential forms
  • degenerate forms like points. Additionally, note that these curve forms may be categorized orthogonally by other characteristics such as open, closed, degenerate and
  • Profile curves include curves from the following curve-type categories (2.3.1) through (2.3.5).
  • Closed curves delimit regions of, e.g., a surface, and are especially useful for setting
  • a label surface is a region that must be of a particular surface type, denoted a
  • Each such label surface is highly constrained and is
  • Fig.8 shows an elliptic region 100 blended into a cylinder 108, wherein the closed curve 110 delimits the elliptic
  • a closed curve may often match tangencies at end points.
  • an open curve may be of zero length, or a closed
  • a point blend created from blending between a degenerate circular disk (i.e., the point labeled S,) and the cylinder 116 (also
  • a surface can be generated that blends between a plurality of points (i.e., degenerate profiles) and an
  • FIGs. 23 and 24 show additional blends to degenerate profiles.
  • Fig.23 shows a blended surface 710 that extends between the degenerate profile (point) 714, and the circular end 718
  • the blended surface 710 is a blending of the isocline ribbons 726 and 730, wherein the isocline
  • ribbon 726 is a planar disk having the degenerate profile 714 as its center point, and the isocline ribbon 730 has the circular end
  • Fig.24 shows another blended surface 750 that extends between the degenerate profile (point) 754, and the planar
  • annulus 758 having a circular curve 760 therein (and having, optionally, a central hole 762 therethrough with curve 760 as its
  • the blended surface 710 is a blending of the isocline ribbon 766 (for the degenerate profile 754), and
  • the annulus 758 (which, e.g., can optionally be an isocline ribbon to the surface 770 wherein curve 760 is a profile).
  • S be the isocline ribbon 766 and S 2 be the annulus 758, the distance-like measurements (in their corresponding parameter spaces)
  • curves are general curve forms that include other curves as sub-curves, wherein the sub-curves may cross or may kink, e.g., at
  • Fig. 10 shows a composite curve 120 that includes two crossing sub-curves 124 and 128.
  • a composite curve 120 that includes two crossing sub-curves 124 and 128.
  • curves can also have their sub-curves strung end-to-end.
  • D(p) can be used as the input to a blending function, B(D), for blending one or more surfaces to the
  • the present invention allows a surface to be "trimmed," wherein trimming refers to a process for constraining or
  • the pre-image of a trim curve e.g., in the (u,v) parameter space of the surface, identifies the extent of the pre-image
  • a trim curve may be a profile curve, and the desired trimmed surface is that
  • the original untrimmed surface is the generally rectangular portion 130.
  • the rounded surface 134 is a "label" surface
  • trim profile 138 may have an associated isocline ribbon
  • the present invention may include a trimming technique to create a hole in a geometric object.
  • a hole can be constructed that can be used, e.g., as a handle of a
  • a parameter space curve may be quite simple and still be the pre-image of a
  • I may be a straight line.
  • This section describes a variety of methods for calculating a distance-like measurement (more generally, a monotonic
  • each ribbon is parametric and has, e.g., the planar unit square [0,l]x[0,l] as the common parameter space for the ribbons.
  • One distance-like function capable of being used for blending is a function that is dependent on only one or the other coordinate of
  • a triangular domain in parameter space bounded by, e.g., three profile curve pre-images (that are also curves) can be
  • the r, s, t parameters are called "barycentric coordinates"* ⁇ are used
  • the distance to the four profile pre-image boundaries in parameter space can be u, v, I -u,
  • v 3 , v 4 and v 5 may be utilized, wherein the profile pre-images are the heavy lines labeled 149a through I49e.
  • first stellate, i.e., make a star from, the pre-image polygon 148 by extending each of the sides 149a
  • measurements are the lengths of the line segments 153a through 153e from p to the sides 149a through I49e of the polygon 148.
  • the distance-like measurements can be normalized.
  • Conies include parabolas, hyperbolas and ellipses.
  • the general form of a conic is
  • Formula (8) can be used regardless of whether the conic is represented implicitly or parametrically.
  • the value of the offset distance that forces the offset to go through the point is the distance measurement for that
  • this distance-like measurement may be worthwhile in that it is robust (i.e., not ill-
  • the present invention also includes a novel technique for computing a distance-like measurement on complex curves
  • each patch 168 can be considered as a second
  • sub-curves 160a and 160b that are joined at their endpoints by the same two segments 164), simple functions f,(s) and
  • parameters u and v can both be represented as Bezier functions of s and t.
  • parameters u and v can both be represented as Bezier functions of s and t.
  • s and t can be considered as a pre-image parameter space for the parameter space 158 wherein the pre-image of curve 160a is
  • Figure 17 shows a block diagram of the typical flow of design construction operations performed by a user of the present
  • profile handles may be needed to construct an associated profile, and the profile is required to construct the
  • the isocline ribbon may be required to obtain the desired shape of the associated object (e.g., a
  • Figs. 26 through 30 provide a high level description of the processing performed by an embodiment of the present
  • a user of the present invention can efficiently perform iterative approximations to a geometric object being designed without
  • portions of such objects may be satisfactorily designed using a wide range of geometrically shaped objects. Accordingly, the
  • present invention allows many of these geometric objects to be designed without the user having to needlessly specify precision
  • step 1004 the end points and tangents
  • TAN I and TAN2 are assigned to the variables TAN I and TAN2, respectively. Note that PTI, PT2, TAN I and TAN2 can be supplied in a variety of
  • one or more of these variables can have values assigned by a user and/or one or more may be derived from
  • TAN I and TAN2 may be determined automatically according to a parameterization of
  • a geometric object e.g., a surface upon which the points PTI and PT2 reside.
  • steps 1008 and 1012 the blending functions B, and B 2 are selected as discussed in Section (2.1) hereinabove. Note,
  • blending functions provided may be defaulted to a particular pair of blending functions so that a user may not
  • the high precision and/or small scale design features may be incorporated into a user design only where necessary.
  • step 1016 the interpolating curve, C(u), is computed using a variation of Formula (2) applied to a one-dimensional
  • ribbon boundary definition for a portion of the object S between PTI and PT2 depending on, e.g., how smooth the object is along
  • step 1104 of Fig.27 the curve interpolation program represented in Fig.26 is invoked with PTI, PT2 and
  • a tangent i.e., a picket
  • isocline ribbon points corresponding to PTI and PT2 are determined and assigned to the variables, RIBBON PTI and
  • the isocline ribbon approximation bounded by the interpolating (profile) curve C(u), the corresponding pickets (PICKETI and PICKET2), and the newly generated isocline boundary R(u) does not necessarily form a
  • the curves, C(u) and R(u) may be substantially coincident (e.g., if PICKETI is identical to TANI, and PICKET2
  • FIGs.28A and 28B a flowchart for a program is provided for constructing a more precise isocline ribbon boundary
  • variable MARKER SET wherein these markers are on the surface, S, and the markers are ordered according to their desired
  • the markers are generally provided (e.g.
  • tangents to the surface S corresponding to the markers M are tangents to S entered by the user.
  • such tangent vectors may be provided automatically by, for example, determining a tangent of the
  • step 1208 of Fig.28A the first marker in the set, MARKER SET, is assigned to the variable, MARKERI. Subsequently,
  • step 1212 a determination is made as to whether there is an additional marker in MARKER SET. If so, then in step 1216, the
  • variable, INTRVL is assigned a parametric increment value for incrementally selecting points on the profile curve(s) to be
  • INTRVL may be assigned a value in the range greater than or equal
  • step 1220 the variable, MARKER2, is assigned the value of the next marker in MARKER SET. Subsequently, in step 1220, the variable, MARKER2, is assigned the value of the next marker in MARKER SET. Subsequently, in step 1220, the variable, MARKER2, is assigned the value of the next marker in MARKER SET. Subsequently, in step 1220, the variable, MARKER2, is assigned the value of the next marker in MARKER SET. Subsequently, in step 1220.
  • step 1228 an isocline boundary approximation is determined according to Fig. 27 using the values of MARKERI , MARKER2 and the interpolating curve, C(u), for obtaining the isocline boundary approximation
  • step 1240 the variable, u VAL, is assigned the initial default value I NTRVL for selecting points on the
  • step 1244 the variable INCRMT PT is assigned the point corresponding to C,(u_VAL).
  • step 1245 the variable, S_PT, is assigned a point on S that is "closest" to the point C (u_VAL) More precisely,
  • step 1246 a determination is made as to whether the point INCRMT_PT is within a predetermined distance of S_PT (e.g., the
  • predetermined distance may be in the range of I0 "3 to 10 ).
  • the predetermined distance may be user set and/or
  • step 1248 is encountered wherein
  • step 1252 an approximation to an isocline picket at C,(u_VAL) is determined and assigned to the variable,
  • step 1254 the tangent to the surface (more generally, object) S at the point C,(u_VAL) is determined and assigned
  • step 1256 a determination is made as to whether the vectors, INCRMT_TAN and PICKET are sufficiently close to one
  • step 1268 a determination is made as to whether the end of
  • step 1244 is again encountered, and some or all of the steps through 1256 are performed in determining
  • step 1246 note that if INCRMT PT is not close enough to S, then an interpolating curve more finely
  • step 1272 is performed wherein a marker is generated for the point, S_PT,
  • step 1276 the marker currently denoted by MARKER2 is flagged as unused (step 1276), and in step 1280, the most recently constructed
  • step 1220 and subsequent steps are deleted.
  • steps 1272 through 1280 and step 1220 are also performed if in step 1256, INCRMT JAN and PICKET are not
  • MARKER_SET is determined and various of the steps 1220 and beyond are performed. That is, in step 1284, MARKERI
  • C (u) C (0)
  • C (I) C N (I).
  • Figs. 29 and 30 provide high-level descriptions of flowcharts for modifying one or more surfaces (more generally
  • subsurfaces S
  • ( i 1 ,2,...N, N ⁇ I , where these subsurfaces S, are connected to one another (e.g., patched together) along
  • the modifications to the subsurfaces are computed and displayed in real-time as the user enters the modifications to
  • the present invention has reduced this overhead by providing a novel
  • step 1400 if there are not profiles and isocline
  • the isocline handles and ribbon tangents corresponding to markers on the surface S 0 are graphically displayed to the user.
  • step 1408 a determination is made as to whether the user has requested to add one or more additional isocline ribbons to the
  • step 1412 If the user has made such a request, then step 1412
  • markers are added: (a) whenever a profile contacts a boundary of a subsurface S exertion and (b) so that profile curves will be extended in a manner that terminates each one on
  • step 1420 following step 1 16, all newly added isocline handles and ribbon tangents are displayed. Note that in some
  • only the isocline handles are displayed initially, and the user is able to selectively display the ribbon tangents as
  • step 1424 a determination is made as to whether the user has requested to add one or more additional
  • a profile with one or more additional markers should, in general, conform more closely
  • step 1432 the additional new markers and optionally, their corresponding isocline handles and ribbon
  • tangents are graphically displayed to the user.
  • steps 1408 through 1420, and steps 1424 through 1432 are performed sequentially.
  • each new marker can be performed individually and displayed prior to obtaining a next new marker location from the user.
  • consecutive executions of the steps 1408 through 1420 may be interleaved with one or more executions of the steps 1424 through
  • step 1436 a determination is made as to whether an isocline handle and/or a ribbon tangent is selected by the user
  • step 1440 the marker corresponding to ISO is determined and access thereto is provided via the variable, MRKR.
  • step 1444 the collection of one or more subsurfaces S shield...,S N adjacent to MRKR are determined and access to these
  • ADJ SURFACES adjacent subsurfaces
  • step 1452 a collection of surface boundary representations denoted MOD SET (step 1456).
  • MOD SET a collection of surface boundary representations denoted MOD SET
  • step 1464 the program of Fig.30 is invoked for modifying, in real-time as the user modifies ISO, the portion
  • step 1504 the first (next) modified version of the isocline handle and/or ribbon tangent corresponding to the
  • step 1508 all isocline ribbons containingthe modified isocline
  • step 1512 the first (next) boundary representation in MOD_SET is assigned to the variable, B.
  • step 1516 the set of isocline ribbons for the (profile) boundary segments contained in B are assigned to the variable, A Note
  • step 1520 a blended surface is generated that is delimited by the profiles of the isocline ribbons of R.
  • the portion of a parameter space used in generating the surface, S(p), of this step may have two, three, four,
  • step 1524 the surface S(p) is displayed, and in step 1528 a determination is made as to whether there
  • step 1512 is an additional boundary representation in MOD SET for generating an additional blended surface S(p). If so, then step 1512
  • step 1532 a determination is made
  • a user interface may be provided for defining isoclines.
  • a designer may, for example, require that an isocline be perpendicular to a given light direction along
  • interface may allow for various constraints to be input for generating isocline ribbons, isocline handles and/or ribbon tangents
  • the user interface allows for global constraints such as light direction, curvature,
  • the user will start with a given geometric object, for example a cylinder.
  • the user may then inscribe a profile curve on the cylinder by placing markers at various points on the cylinder.
  • the profile tangents and/or isocline handles may be defaulted by adopting the slope information from the cylinder. For example, at each marker, the profile tangents are in the plane tangent to the cylinder at the marker.
  • the user may then select and modify the markers, add additional markers, and/or modify the position and the direction of the markers
  • isocline handles and/or ribbon tangents.
  • the isocline ribbon is accordingly modified, the cylinder (more generally, geometric
  • step 1908 the user constructs a profile curve on the selected surface (object).
  • step 1912 an isocline ribbon (or at least the isocline boundary) is generated for the profile. Note that
  • this ribbon/boundary can, if desired, be generated substantially without additional user input. That is, an isocline ribbon/boundary may be generated from the tangency characteristics of the surface upon which the profile resides.
  • the parametric tangents on the surface at points on the profile can
  • first isocline ribbon/boundary for a first surface having the profile, and if the profile is on the seam
  • the isocline ribbon/boundary may also optionally
  • the generated isocline ribbon/boundary may be used to modify the surface(s) having the profile curve
  • an operation is provided to the designer wherein a common boundary
  • continuity criteria e.g., curvature continuity
  • that of tangent plane continuity e.g., curvature continuity
  • darts i.e., surfaces that are smooth except at a single point, where the surface kinks
  • Such operations can be performed using the present invention by positioning profile curves on the surface on opposite sides of a sharp edge and blending smoothly between the profiles (e.g., using Formula (I) as described in
  • Explicit profiles are the profile curves that express a designer's intent. Explicit profiles may be unconstrained
  • Implicit profiles may be visible boundaries between surface patches caused, for example
  • a surface discontinuity i.e., a kink or curve defined between an end surface of a cylinder and the cylindrical side
  • Implicit profiles are created automatically when the user introduces, e.g., a surface discontinuity. All profiles in a
  • Profile markers and handles are created in the following ways:
  • a marker may be identified with a plurality of coincident points on the same profile (e.g. a profile that loops back and
  • Profile markers inserted by the designer may be inserted for providing profile handle points, or for setting specific

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Abstract

L'invention concerne un procédé et un système de conception assistée par ordinateur (CAO) destinés à concevoir des objets géométriques tels que des surfaces (62a, 604). La présente invention procède à des interpolations et/ou mélanges parmi une pluralité initiale d'objets géométriques (30, 34). Le mélange est suffisamment rapide pour que des déformations en temps réel de ces objets mélangés se produisent lors de l'introduction de données de déformation. Ainsi, un utilisateur effectuant une conception à l'aide de la présente invention obtient un retour immédiat aux modifications d'entrée sans saisir séparément de commande d'exécution de ces déformations. De nouvelles techniques de calcul sont utilisées pour mélanger des objets géométriques (30, 34) dans lesquelles des sommes de points pondérées sur les objets géométriques sont utilisées pour dériver un nouvel objet géométrique mélangé (62a, 604). La présente invention est applicable à divers domaines de conception tels que, par exemple, la conception de bouteilles, de véhicules et de bateaux et permet également une animation efficace par modification répétée des surfaces d'un objet animé tel qu'une représentation d'une face.
PCT/US1999/016844 1999-07-23 1999-07-23 Systeme de conception et de modelisation geometriques utilisant une geometrie de controle Ceased WO2001008102A1 (fr)

Priority Applications (9)

Application Number Priority Date Filing Date Title
MXPA02000845A MXPA02000845A (es) 1999-07-23 1999-07-23 Diseno geometrico y sistema de modelado utilizando geometria de control.
HU0700118A HUP0700118A2 (en) 1999-07-23 1999-07-23 Method for determining a blended geometric object, for generating a geometric object on a computational system, and for generating, modifying a representation of a geometric object, as well as for modifying the representation of a surface
EP99939655A EP1210692A4 (fr) 1999-07-23 1999-07-23 Systeme de conception et de modelisation geometriques utilisant une geometrie de controle
CA002379459A CA2379459A1 (fr) 1999-07-23 1999-07-23 Systeme de conception et de modelisation geometriques utilisant une geometrie de controle
JP2001513115A JP2003505800A (ja) 1999-07-23 1999-07-23 制御幾何（コントロールジェオメトリ）を用いた幾何学的設計およびモデリングシステム
AU53907/99A AU5390799A (en) 1999-07-23 1999-07-23 Geometric design and modeling system using control geometry
CN99816901A CN1391683A (zh) 1999-07-23 1999-07-23 使用控制几何的几何设计和建模系统
PCT/US1999/016844 WO2001008102A1 (fr) 1999-07-23 1999-07-23 Systeme de conception et de modelisation geometriques utilisant une geometrie de controle
KR1020020004000A KR20020021800A (ko) 1999-07-23 2002-01-23 제어 기하학을 이용한 기하학적 디자인 및 모델링 시스템

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EP1881457A1 (fr) * 2006-07-21 2008-01-23 Dassault Systèmes Méthode de création d'une surface paramétrique symétrique par rapport à une opération de symétrie donnée
US7589720B2 (en) * 2004-08-04 2009-09-15 Microsoft Corporation Mesh editing with gradient field manipulation and user interactive tools for object merging
US7636091B2 (en) 1998-07-23 2009-12-22 Freedesign, Inc. Computational geometry using control geometry having at least two dimensions
FR2937770A1 (fr) * 2008-10-27 2010-04-30 Snecma Procede de creation d'une surface non axisymetrique
US7742901B2 (en) 2002-08-22 2010-06-22 British Telecommunications Public Limited Company Method and system for virtual object generation
US7868885B2 (en) 2007-06-22 2011-01-11 Microsoft Corporation Direct manipulation of subdivision surfaces using a graphics processing unit
CN103186516A (zh) * 2011-12-29 2013-07-03 广州市中海达测绘仪器有限公司 一种生成监测图表的方法、装置及系统
WO2014113241A1 (fr) * 2013-01-15 2014-07-24 General Electric Company Procédé, système et produit d'ordinateur pour analyse d'objet non-destructrice
US8836701B1 (en) 1998-07-23 2014-09-16 Freedesign, Inc. Surface patch techniques for computational geometry
US9196090B2 (en) 2012-05-02 2015-11-24 Dassault Systemes Designing a 3D modeled object
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US10108752B2 (en) 2015-02-02 2018-10-23 Dassault Systemes Engraving a 2D image on a subdivision surface
US10255381B2 (en) 2014-12-23 2019-04-09 Dassault Systemes 3D modeled object defined by a grid of control points
CN111414662A (zh) * 2020-03-31 2020-07-14 北京市建筑设计研究院有限公司 利用直线型材拼装带状曲面建筑表皮的方法
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US7196702B1 (en) 1998-07-23 2007-03-27 Freedesign, Inc. Geometric design and modeling system using control geometry
US7755623B2 (en) 1998-07-23 2010-07-13 Freedesign, Inc. Computational geometry using control geometry having at least two dimensions
US9262859B2 (en) 1998-07-23 2016-02-16 Freedesign, Inc. Surface patch techniques for computational geometry
US7417635B2 (en) 1998-07-23 2008-08-26 Freedesign, Inc. Computational geometry using control geometry having at least two dimensions
US8836701B1 (en) 1998-07-23 2014-09-16 Freedesign, Inc. Surface patch techniques for computational geometry
US7636091B2 (en) 1998-07-23 2009-12-22 Freedesign, Inc. Computational geometry using control geometry having at least two dimensions
US11403434B2 (en) 1998-07-23 2022-08-02 Cad-Sense Llc Surface patch techniques for computational geometry
US7236167B2 (en) 1998-07-23 2007-06-26 Freedesign, Inc. Computational geometry using control geometry having at least two dimensions
US7742901B2 (en) 2002-08-22 2010-06-22 British Telecommunications Public Limited Company Method and system for virtual object generation
US7589720B2 (en) * 2004-08-04 2009-09-15 Microsoft Corporation Mesh editing with gradient field manipulation and user interactive tools for object merging
US7893937B2 (en) 2006-07-21 2011-02-22 Dassault Systemes Method for creating a parametric surface symmetric with respect to a given symmetry operation
EP1881457A1 (fr) * 2006-07-21 2008-01-23 Dassault Systèmes Méthode de création d'une surface paramétrique symétrique par rapport à une opération de symétrie donnée
US7868885B2 (en) 2007-06-22 2011-01-11 Microsoft Corporation Direct manipulation of subdivision surfaces using a graphics processing unit
US11907617B2 (en) 2008-07-18 2024-02-20 Cad-Sense Llc Surface patch techniques for computational geometry
FR2937770A1 (fr) * 2008-10-27 2010-04-30 Snecma Procede de creation d'une surface non axisymetrique
US8744823B2 (en) 2008-10-27 2014-06-03 Snecma Computer aided design method for creating a surface in a complex system
WO2010049636A1 (fr) 2008-10-27 2010-05-06 Snecma Procede de conception assistee par ordinateur pour creer une surface dans un systeme complexe
CN103186516A (zh) * 2011-12-29 2013-07-03 广州市中海达测绘仪器有限公司 一种生成监测图表的方法、装置及系统
US9196090B2 (en) 2012-05-02 2015-11-24 Dassault Systemes Designing a 3D modeled object
WO2014113241A1 (fr) * 2013-01-15 2014-07-24 General Electric Company Procédé, système et produit d'ordinateur pour analyse d'objet non-destructrice
US9042634B2 (en) 2013-01-15 2015-05-26 General Electric Company Method system and computer product for non-destructive object analysis
US10255381B2 (en) 2014-12-23 2019-04-09 Dassault Systemes 3D modeled object defined by a grid of control points
US10108752B2 (en) 2015-02-02 2018-10-23 Dassault Systemes Engraving a 2D image on a subdivision surface
US11144679B2 (en) 2015-02-02 2021-10-12 Dassault Systemes Engraving a 2D image on a subdivision surface
US20180101503A1 (en) * 2016-10-07 2018-04-12 Ford Global Technologies, Llc Method and device for assessing signals
CN107918691A (zh) * 2016-10-07 2018-04-17 福特全球技术公司 用于评估信号的方法和装置
CN111414662A (zh) * 2020-03-31 2020-07-14 北京市建筑设计研究院有限公司 利用直线型材拼装带状曲面建筑表皮的方法

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EP1210692A4 (fr) 2006-02-08
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