EP1820160A1

EP1820160A1 - Method for producing technical drawings from 3d models using at least two colliding 3d bodies

Info

Publication number: EP1820160A1
Application number: EP05815359A
Authority: EP
Inventors: Manfred Göbel; Hans-Ulrich Becker; Jochen DÜRR
Original assignee: CoCreate Software GmbH and Co KG; COCREATE SOFTWARE GmbH
Current assignee: PTC Inc
Priority date: 2004-12-10
Filing date: 2005-12-06
Publication date: 2007-08-22
Also published as: US20090096785A1; JP2008523481A; US8154545B2; DE102004062361A1; JP4592758B2; WO2006061185A1; DE102004062361A8

Abstract

The invention relates to a method and a computer-aided modelling system for creating a technical drawing from at least two modelled 3D bodies that collide with one another. In a first step, one or more of the regions of the 3D bodies that are affected by the collision are selected. In a second step, a group of colliding faces of the selected regions of the two or more 3D bodies are combined to form a respective collision group and a technical drawing of the two or more colliding modelled 3D bodies is produced. A 2D edge or its associated boundary of a face that belongs to a collision group is treated by masking the other faces that are associated with the same collision group.

Description

Method for deriving technical drawings from 3D models with at least two colliding 3D bodies

The present invention relates to a method and a corresponding computer-aided modeling system for deriving technical drawings of 3D models with at least two 3D bodies colliding with each other. Furthermore, the present invention comprises a corresponding computer program and a computer program product.

Computer-aided geometric modeling is generally concerned with the construction, manipulation and imaging of three-dimensional geometric objects for applications such as construction, design, fabrication, visualization, photorealistic graphics and also so-called "special effects" in films.

With the help of so-called 3D CAD systems (Computer Aided Design) it became possible to create a three-dimensional description of 3D bodies instead of two-dimensional drawings. From this, a computer can not only generate arbitrary two-dimensional views, but also make the data usable for the numerical simulation / analysis of the constructed objects. Simulation data obtained thereby can be used, for example, in numerically controlled production machines, which produce a desired 3D object therefrom. Creating 3D bodies in the CAD system is also referred to as solid modeling. Today, in many cases, it is still common and necessary to produce technical drawings, ie 2D models or 2D model views, from given 3D models, which are used, for example, in the production of the 3D objects. In the 3D mode Assembly of assemblies (groups consisting of several 3D bodies) may be due to inaccuracies in the design or intentionally to colliding, ie interpenetrating, 3D objects or 3D bodies.

A collision is understood below to mean that two 3D bodies collide if their intersection has a positive volume. It is said that a lot of 3D bodies collide when at least two of these 3D bodies collide with each other.

There are several methods to represent 3D bodies in a 3D CAD system. The most well-known method is the so-called BRep method ("Boundary Representation Method"). In this case, a 3D body is essentially described by its oriented edge surfaces.

To describe a BRep model you need geometry and topology elements. Geometry elements are objects that are given by an analytical description. Geometry elements in Solid Modeling are points, curves, and surfaces. Topology elements link the geometric data or geometric and topological data together. Typical topology elements that are necessary to describe a BRep model are corners, margins and margins. For better model structuring, surface edges, surface edge curves and polysurfaces are also used. Some topology elements, such as Edge edges and edge surfaces restrict a geometric object in its domain of definition. With the help of topology and geometry elements, 3D bodies can be clearly represented.

For a better understanding, geometry and topology elements are briefly described below. Points are 3D objects that are typically described by their x, y, and z coordinates.

Curves are 3D objects that are represented in parametric form. Simple analytical curves are e.g. Straight lines, circles, ellipses, etc. Complicated curves ("free-form curves") are e.g. represented by (rational) spline curves.

Surfaces are 3D objects with a well-defined orientation, usually in parametric form. Surfaces are eg simple analytical surfaces such as plane, cylinder, cone, sphere, torus, etc .; more complicated surfaces ("free-form surfaces") are usually represented by so-called (rational) so-called spline surfaces. Some 3D modelers also describe simple analytic surfaces through implicit equations. An implicit description of a cylinder is given, for example, by x ^Λ 2 + y ^A 2 = 1.

The curves and surfaces used in the BRep plot typically have smooth (i.e., at least continuously differentiable) and regular parametrizations. Singularities are also allowed at edge points.

Corners (vertices) are geometrically described by dots. Corners always belong to a marginal edge.

Edges are described geometrically by curves bounded by a start or end corner. For example, a straight edge between two points A and B is represented by a straight line and by the additional specification of the starting point A and the end point B. A and B are in this case the corners of the peripheral edge. Edge- Edges have the same or opposite orientation as their descriptive curves.

A surface edge (coedge) is described by a marginal edge that lies on a surface. The orientation / flow direction of the surface edge may be different from the orientation / flow direction of the peripheral edge. Surface edges always belong to a plane edge.

Surface contours (loops) are closed "curves", consisting of one or more surface edges, all of which have the same direction of flow. The start corner of the first surface edge corresponds to the end corner of the last surface edge; every corner of a loop has exactly two adjacent surface edges. Surface edges always belong to a border area.

Edge surfaces / faces are geometrically represented by orientable surfaces together with their bounding surface edges. Edge surfaces have the same or opposite orientation as their descriptive surfaces. The orientation is determined by the so-called right-screw rule, i. an enclosed surface area lies in the direction of the circumference left of its surface edges. A face can be bounded by one or more loops (border area with or without "holes"). Edge surfaces are contiguous surface pieces. They always belong to a polysurface.

Shells are contiguous sets in 3D that are typically described by multiple edge surfaces that have a consistent surface orientation.

This means that all boundary surface normals point either to the "inside" or to the "outside" of the shell. Put shells usually closed topological two-dimensional manifolds; these are referred to below as "unifold" shells. In particular, each marginal edge of a "manifold" shell lies on exactly two edge surfaces.

3D bodies can consist of one or more shells. All edge surfaces, margins and corners occurring on a 3D body can be directly addressed. A 3D body is completely described by its boundary surfaces.

So-called "manifold" bodies are 3D bodies that are bounded by one or more "manifold" shells. Self-penetrating edge surfaces, margins and polysurfaces are not allowed in the modeling of manifold bodies.

BRep models are defined by one or more boundary elements or polysurfaces or shells. The BRep representation is an intuitive and practicable method for representing real 3D bodies within a CAD system.

So-called "manifold" BRep models are BRep models constructed from one or more manifold bodies. Most of the 3D bodies occurring in the application (mold making, mechanical engineering, design, etc.) can be represented in this way via their boundary elements as a computer model.

Volume models allow a variety of evaluations. For example, a solid modeler can provide algorithms for determining the volume, surface area, center of mass, or moment of inertia of a 3D body. Other methods lead geometric position tests between a 3D body and other geometric objects.

A derivation of technical drawings or a layout calculation from one or more predefined "manifold" bodies means the generation of a 2D model of these 3D bodies by means of parallel or central projection into a predefined projection plane. Simplified, the 2D edges created by projection are classified as "invisible" to a hidden edge; otherwise a 2D edge is "visible". A more detailed explanation will be given later.

Parallel projection means a projection of corresponding 3D elements orthogonal to the projection plane, and under central projection the projection of the 3D elements from a certain point, a so-called "eye point" outside the projection plane into the projection plane. The most commonly used parallel projection in Solid Modeling applications is a special case of central projection, where you can imagine that the "eye point" is at infinity.

Based on a BRep representation of one or more 3D bodies, the layout calculation is performed in the following steps:

1. Calculation and imprint of silhouette edges in the corresponding border areas. A surface point P is a silhouette point if, in the case of a parallel projection, the boundary normal N (P) belonging to the point P is perpendicular to the projection direction V. In central projection, the connection vector between "eye point" E and surface point P is perpendicular to the edge normal N (P). By memorizing the silhouettes etten the edge surfaces usually disintegrate into several edge surface pieces. Each such edge face piece has the property that, in the case of parallel projection, for all inner points P with their associated edge normal N (P) of this edge face piece, either <V, N (P)>> 0 or <V, N (P)><0 applies. In this case, <.,.> Denotes the eucidal standard scalar product in 3D.

Edge face pieces with the property <V, N>> 0 for all inside edge normal N are called front faces and edge face pieces with the property <V, N> <0 for all inside edge normal N are called back faces.

The same applies to the central projection.

2. Projection of all given 3D body edges (possibly separated by silhouette curves) including the silhouette curves in the projection plane. The projected 2D curves are then blended and possibly separated.

A consequence of the first two steps is that all generated and possibly split 2D edges have definite visibility under certain conditions explained in more detail below. A 2D edge is visible when the corresponding section of the associated (3D) edge is visible, ie when a viewing beam emanating from an inner point of the edge edge section in the direction of the "eye points" does not hit or intersect the 3D model at any other edge point. The 2D edge is invisible if the corresponding section of the associated (3D) edge is invisible. 3. Determination of the visibility by a so-called visual beam method. For each 2D edge, the center is first determined, and then the corresponding 3D point Q is determined on the edge closest to the "eye point". Then, a visual ray is built from the test point Q to the "eye point", and the 2D edge is classified as visible if this ray does not hit or cross another edge point of the 3D model. Otherwise, the 2D edge is invisible.

The computation of the layout for complex 3D models can be accelerated by a variety of algorithmic optimizations, e.g. the following:

• To determine the visibility, it is sufficient to look only at the "front faces".

• An edge on two "back faces" is never visible.

• In order to minimize the resulting layout during the projection and blending step, wherever possible, "unnecessary" separation of 2D edges is avoided. For example, the projection of a border on two "front faces" never contributes to the separation of another 2D edge.

• The generally relatively expensive determination of the visibility of a 2D edge by the described visual beam method can be optimized by rapid so-called visbility propagation rules.

The clear visibility of all generated and possibly separated 2D edges and the above mentioned optimizations are correct and possible if and only if given model consists of one or more "manifold bodies" that do not collide with each other. Otherwise, the determination of the visibility of 2D edges described herein will generally result in false visibility classifications, and the visibility inheritance rules may then, as a consequence, lead to a large number of misclassified 2D edges. Thus, for example, in the case of two colliding 3D bodies, marginal edges of a 3D body may exist which, due to the collisions, "penetrate" into the other 3D bodies, and therefore have both a visible and an invisible area. A clear determination of visibility is obviously not possible for such marginal edges in general. For example, classifying such an edge or its 2D projection as visible / invisible (which is just as wrong as classifying it as invisible / visible) may lead to many 2D edges being mistakenly visible due to algorithm optimization, eg visibility rules / invisible classified.

The standard method described above for determining a technical drawing based on manifold BRep models is a so-called hidden-line algorithm. The different forms of this standard method differ essentially by a different representation of geometry and topology elements and by the interaction of the possible algorithm optimizations. Thus, e.g. analytical or graphical model representations are possible, which differ essentially by their geometrical presentation.

Based on the described prior art and the associated problems, the present invention proposes for the calculation or preparation of technical drawings of at least two colliding modeled 3D Give bodies a new approach to visibility on a face-face level.

The invention provides a method for deriving a technical drawing of conflicting "manual bodies" with the features of claim 1, with the help of which display errors in overlapping or colliding 3D bodies are avoided or minimized. Furthermore, the present invention comprises a computer-aided modeling system with the features of claim 5.

The inventive method is particularly suitable for the treatment of so-called micro-collisions, i. of collision whose collision cut amount has a very small volume.

According to claim 1, a method for deriving a technical drawing of at least two mutually colliding "manifold bodies" or 3D bodies is proposed, wherein at first selectively one or more affected by the collision areas of the colliding 3D bodies are determined and marked. Then, colliding edge surfaces of the selectively determined regions of the at least two 3D bodies are grouped into a respective collision group. Then, a derivation of a technical drawing of the at least two 3D bodies colliding with each other is performed, wherein a 2D edge or its associated edge of a collision group associated edge surface is treated by masking the other same collision group associated edge surfaces. The modeled 3D bodies can be generated, for example, with a BRep modeler already described at the beginning.

In a further possible embodiment of the method according to the invention, a marginal edge of an edge surface associated with a collision group is treated with respect to the visibility of the marginal edge while blanking out the other edge surfaces associated with the same collision group. This is done, for example, in such a way that individual algorithm optimizations are selectively restricted during the layout calculation for areas of the 3D bodies affected by the collision and accordingly suitably marked and marked; such as e.g. Visibility inheritance rules are not applied to these 3D bodies or the correspondingly marked areas.

After the projection and interleaving step described at the beginning or immediately before the visibility calculation of the 2D edges also described at the outset, all the associated colliding pairs, in this case, for example, are designated for the marked colliding 3D body pairs, here for example as (Kl, K2) (Fl, F2), determined from edge surfaces, wherein Fl belongs to the first 3D body Kl and F2 to the second 3D body K2. The actual visibility determination for a 2D edge whose edge e closest to the "eye point" belongs to a marked colliding 3D body K and whose edge e belongs to an edge surface F that is referenced in at least one of the colliding pairs of edge surfaces then runs For example, according to the following central rule:

The 2D edge or its associated boundary edge is classified as visible if and only if the sighting beam for visibility determination of this 2D edge no further point of the entire 3D model, whereby all edge surfaces Fi of 3D bodies different from the 3D body K, which collide with F, are ignored or hidden in the visibility test.

Otherwise, the 2D edge is invisible. For visibility purposes, it is sufficient to consider only the front facets. This procedure leads to unique, independent of the test sequence visibility classifications for 2D edges whose associated margins are involved in collisions. All other 2D edges are classified according to the previously described standard visual beam method.

The described method for the treatment of collisions has an effect only in an environment of the colliding edge surfaces. Therefore, micro-collisions will only be very local, i. the 2D edges affected by the collision will be uniquely classified and the remaining collision-free part of the technical drawing will remain unaffected by the special treatment. In general, in micro-collisions, it can be said that the technical drawing for two micro-colliding 3D bodies differs only insignificantly from a corresponding collision-free situation with two touching 3D bodies.

Further, the present invention comprises a computer-aided modeling system for creating a two-dimensional drawing of at least two colliding modeled manifold bodies having an input unit for inputting commands and data for generating and modifying the two colliding 3D bodies, a modeling unit for Calculating the two colliding 3D bodies, a functional unit for determining collision-related regions of the at least two 3D bodies, a grouping unit for grouping colliding edge areas of the collision-affected areas into a collision group, a projection unit for calculating a technical drawing, and a selection unit for selectively masking individual colliding edge areas associated with a collision group.

The present invention also includes a computer program with a program code to perform all the steps of a method according to the invention when the computer program is executed on a computer or a corresponding computing unit.

The ^'present invention also relates to a computer program product with a program code stored on a computer legible data carrier to carry out an inventive method when the computer program is executed on a computer or a corresponding computing device.

Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawings.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the particular combination given, but also in other combinations or in isolation, without departing from the scope of the present invention.

The following three figures show the typical BRep elements as known in the art.

FIG. 1 shows a rough representation of a BRep model on the basis of a cube; FIG. 2 shows a possible representation of a marginal edge;

FIG. 3 shows a typical representation of an edge surface F;

The invention will now be schematically illustrated by way of example in the following drawings and described in detail with reference to the drawings.

Figure 4 shows a possible arrangement of three simple colliding bodies;

FIG. 5 shows the result of a layout calculation carried out with a standard method without special treatment of colliding surfaces;

FIG. 6 shows the result of creating a technical drawing according to an embodiment of the method according to the invention.

FIG. 1 shows a rough representation of a BRep model on the basis of a cube. Part (a) of FIG. 1 shows a sketch of a cube. In (b) the edge surfaces of the cube and in (c) the corners and margins necessary for the description are sketched.

FIG. 2 shows a typical representation of a marginal edge e. The marginal edge e is defined by a curve k. For the edge k e defining curve k, a corresponding flow sense is also drawn. In addition, both an associated (start) corner Vl and an associated (end) corner V2 of the marginal edge e are marked. FIG. 3 shows a typical representation of an edge surface F. The edge surface F is shown with its (oriented) surface S defining it. Furthermore, two so-called loops I ₁ and I ₂ delimiting the edge surface F are shown. The outer loop I ₁ has an orientation in the counterclockwise direction. In contrast, the inner loop I2 has a clockwise orientation and surrounds a "hole" of the edge surface F. At a point P of the edge surface F, a surface normal N associated with the edge surface F is drawn.

FIG. 4 shows a possible arrangement of three 3D bodies colliding with one another, by means of which a possible embodiment of the method according to the invention will be explained in the following FIGURE. In this case, a cylinder, a cuboid and a more general body K is shown. The body K collides with the cylinder and with the cuboid. The cylinder and the cuboid are largely covered by the body K.

FIG. 5 shows the result of a layout calculation of the arrangement sketched in FIG. 4 with a standard method without special treatment of colliding surfaces. Algorithm optimizations such as e.g. Visibility inheritance rules not applied. The margins of cylinder and cuboid marked or marked with "x" are partly visible and partially hidden. This means that their visibility is not clearly classifiable. The previously described visual beam method, which is based on parallel projection, classifies the 2D edges marked with "x" as invisible, since most of the associated 3D boundary edges are hidden.

This result changes abruptly when, while preserving the collisions, the spatial position of cylinder and Cuboid is changed by simple displacement of these bodies in the direction of the cylinder axis out of the body K out. The 2D edges marked with "x" become visible as soon as most of the marginal edges are no longer obscured by the body K.

In FIG. 5, the 2D edges marked with an "o" are correctly classified. However, the application of visibility inheritance rules in such situations would result in unpredictable visibility results.

FIG. 6 shows a result of a preparation of a technical drawing of the 3D bodies which are sketched together in FIG. 4 according to a possible embodiment of the method according to the invention. The procedure or the collision approach here is based on Face-Face-Level. The visibility of the 2D edges marked with "x" is uniquely determined. The edge surface A of the cuboid and the edge surface B of the body K collide with each other. Due to this, the edge surface A and the edge surface B are grouped into a collision group. For example, e.g. the 2D edge (a) visible because it lies on the edge surface A, and this collides with the edge surface B; In addition, the associated edge is hidden by any other non-colliding edge surface. In this case, the visible beam method ignores the edge surface B in the visibility test and thus provides a clear visibility decision for the 2D edge (a); the same applies to all other 2D edges marked with (x). The 2D edges marked with (x) remain visible even when the spatial position of cylinder and cuboid is changed by simple displacement of these bodies in the direction of the cylinder axis out of the body K or into the body K while preserving the collisions.

Claims

claims

1. A method for producing a technical drawing of at least two mutually colliding modeled 3D bodies, comprising at least the following steps: selectively determining one or more collision-affected areas of the at least two 3D bodies,

Grouping mutually colliding edge surfaces of the selectively determined regions of the at least two 3D bodies into a respective collision group,

Performing a derivation of a technical drawing of the at least two colliding modeled 3D bodies, wherein a 2D edge or its associated edge edge of a collision group associated edge surface is treated by masking the other same collision group associated edge surfaces.

2. The method of claim 1, wherein a marginal edge of a collision group associated edge surface is treated with respect to the visibility of the peripheral edge by masking the other same collision group associated edge surfaces.

3. The method of claim 1 or 2, wherein the modeled body are generated by means of a BRep modeler.

4. The method according to any one of the preceding claims, in which affected as the collision areas of minde- At least two 3D body micro-collision areas are selected.

5. Computer-aided modeling system for creating a technical drawing of at least two mutually colliding 3D bodies with an input unit for inputting commands and data for generating and modifying the two colliding 3D bodies, a modeling unit for calculating the two colliding 3D bodies, a functional unit for Determining areas of the at least two 3D bodies affected by a collision, a grouping text for grouping colliding edge areas of the collision-affected areas into a collision group, a projection unit for creating a technical drawing and a selection unit for executing a drawing creation, fading out individual colliding fringes associated with a collision group.

The computerized modeling system of claim 5, wherein the modeling unit is a BRep modeler.

A computer program with program code for performing all the steps of a method according to any one of claims 1 to 4 when the computer program is executed on a computer or a corresponding computing device.

8. A computer program product having a program code stored on a computer-readable medium to perform a method according to any one of claims 1 to 4 when the computer program is executed on a computer or a corresponding computing device.