Abstract:
A system or tool kit is provided that allows a user to specify a deformation for a model. When the deformation produces anomalies the user can select functions or solutions from the tool kit to be executed that correct the anomalies. When the effect of a warp or deformation extends into a region outside a user specified constraint, a clamp function can be selected from the kit to stop the effect outside of the constraint. When a constraint causes the transition from a warp to a non-warp region to result in a sharp transition a tangent continuous transition function can be applied from the kit. When contradictory modifiers and constraints cause unexpected excursions in the warped model, samples with outlier Laplacians can be culled. When the model includes rigid objects, the motion of the rigid objects can be used as a modifier to allow the rigid objects to move with the deformed model without being deformed.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The present invention is directed to a system and method that allows a user to specify a deformation of a model and control that deformation based on conditions associated with the model or specified by the user for the model.  
         [0003]     2. Description of the Related Art  
         [0004]     In performing feature-based deformation of models, such as in the modeling of an automobile, it is often necessary to deal with anomalies that occur in the deformation. What is needed is a set of tools that allow a user to solve the problems associated with these anomalies.  
       SUMMARY OF THE INVENTION  
       [0005]     It is an aspect of the present invention to provide a set of tools that allow a user to fix anomalies that occur during model deformation.  
         [0006]     The above aspect can be attained by a system that allows a user to specify a deformation for a model. When the deformation produces anomalies the user can select functions to be executed that correct the anomalies. When the effect of a warp or deformation-extends into a region outside a user specified constraint, a clamp function can be selected to stop the effect outside of the constraint. When a constraint causes the transition from a warp to a non-warp region to result in a sharp transition, a tangent continuous transition function can be applied. When contradictory modifiers and constraints cause unexpected excursions in the warped model, samples with outlier Laplacians can be culled. When the model includes rigid objects, the motion of the rigid objects can be used as a modifier to augment the deformation so that the deformed model matches seamlessly with the moved rigid objects.  
         [0007]     These together with other aspects and advantages which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]      FIGS. 1-3  depict a simple deformation, an unwanted effect, and the deformation with clamping.  
         [0009]      FIGS. 4-6  show a model, an unwanted effect and a solution for rigid objects.  
         [0010]      FIGS. 7-9  illustrate a simple deformation, an unwanted effect, and the deformation with a tangent constraint.  
         [0011]      FIGS. 10-12  illustrate a simple deformation, an unwanted effect, and the deformation with culling.  
         [0012]      FIG. 13  illustrates a hardware configuration.  
         [0013]      FIGS. 14-20  show additional clamping examples.  
         [0014]      FIG. 21  depicts a clamping process.  
         [0015]      FIG. 22  depicts a clamp function.  
         [0016]      FIGS. 23-25  shows an additional rigid object example.  
         [0017]      FIG. 26  depicts a rigid object process.  
         [0018]      FIGS. 27-31  show additional continuity examples.  
         [0019]      FIG. 32  shows a continuity process.  
         [0020]      FIGS. 33 and 34  show continuity functions.  
         [0021]      FIGS. 35-37  depict a culling example.  
         [0022]      FIG. 38  shows a culling process. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0023]     In a model deformation workflow, a mapping is defined that associates each point in space with a displacement vector. This mapping is used to transform objects such as points, curves and surfaces in space. To deform a model, each point on the model is moved by its associated displacement vector.  
         [0024]     To define a deformation, the user specifies two kinds of data—modifiers and constraints. Both kinds can take the form of loci such as points, curves, or surfaces. A modifier indicates that the deformation is to take a specified origin locus to a specified destination locus. There are two kinds of constraints: a positional constraint indicates that the deformation should not move points on the constraint locus, while a tangential constraint indicates that the deformation should leave both position and orientation unchanged on the constraint locus. Modifiers and constraints are sampled, and a deformation vector is computed for each sample. For constraint samples the deformation vector is zero. For modifier samples the deformation vector is the difference between origin and destination samples. The deformation on the entire space is then computed so as to interpolate or approximate the deformation sample vectors. This can be done, for example, by using radial basis function interpolation, or least squares approximation via a volume spline hierarchy, or a system of partial differential equations. An object that is to be deformed is called a target.  FIG. 1  illustrates a simple deformation setup. A target planar mesh  100  is to be deformed according to modifier  102  going through it. Origin and destination curves are shown. Two constraint lines  104  and  106  are positioned near the left and right boundaries.  
         [0025]     One problem is that, while the interpolation/approximation smoothly interpolates a deformation between modifiers and constraints, the interpolation/approximation creates a global deformation that, in particular, extends beyond the constraints.  FIG. 2  illustrates that the deformation  200  preserves the original mesh position and normal/tangent plane along the constraint  202  on the right. But the deformation also has an unwanted effect beyond the constraint toward the right boundary  204  of the mesh  206 . This is a problem because the user typically intends that the constraints define the boundary of a deformation, and expects the deformation to have no effect beyond those boundaries. The problem is complicated by the fact that in most cases the constraints do not divide space into “inside” and “outside” regions (even though they may so divide a specific model on which they lie).  
         [0026]     A solution to this problem is to supplement deformations with clamping. This solution computes a secondary scalar spatial function—called the “clamp” function. It has a value of: “1” on modifiers and “0” on constraints and “−1” on clampers (clampers will be discussed below). An interpolation/approximation is computed over all space, using methods similar to those for the deformation (e.g. radial basis functions or hierarchical volume splines).  
         [0027]     When the deformation is evaluated at a point, it is set to zero if the clamp function at that point is less than zero. A region in which the clamp function is less than zero is called a clamping region.  FIG. 3  illustrates the same deformation  300 , but with clamping turned on. Now the deformation has no effect to the right of the constraint line  302 .  
         [0028]     In a preferred implementation, the interpolation of the clamp function should be as “linear” as possible. For example, if you are using radial basis functions, the basis functions should be linear. If you are using volume splines, the splines should be linear.  
         [0029]     Sometimes the clamping scheme does not disable the deformation in all regions that the user may wish. By adding additional clampers (usually isolated points), the clamping regions can be enlarged.  
         [0030]     The clamp function will be discussed in more detail later herein.  
         [0031]     One application of deformation technology is design modification and iteration for automotive and industrial design. In these realms, some parts of a design are flexible (i.e. subject to deformation), while others are constrained to be rigid (e.g. a headlight assembly in an otherwise flexible car hood, or a gas cap on the otherwise flexible side of a car). Sometimes constraints are a combination of rigid and flexible—e.g. two lines are constrained to be 3 mm apart, but are otherwise flexible (think of a ribbon, or a cut line for a car door).  FIG. 4  depicts a model  402  that could be a model of a vehicle part such as a passenger enclosure  404  with a cutout or window  406  prior to deformation.  FIG. 5  shows the model  502  after deformation where the bottom has been dragged down to make the enclosure taller. The rigid window  506  has separated from the rest of the enclosure  504 . This is a problem.  
         [0032]     A solution to this problem is to provide deformation-derived movements of the rigid object. In this solution, the rigid object is sampled, and the warp is applied to the samples. Then, a transformation including of a rotation and translation is computed that best approximates the effect of the warp on the samples, in a least squares sense. Then, a new spatial warp is computed, using the rigid object and its transformation as an additional origin/destination modifier pair.  FIG. 6  illustrates a new deformation that modifies the enclosure seamlessly with a rigidly transformed window  606 .  
         [0033]     If there are multiple rigid objects, the above enhancements are carried out for all the objects to create a new warp. One transformation is calculated for each group of objects that are to move as a group.  
         [0034]     Some rigid objects or rigid object groups may be constrained to translate only or rotate only, if the design requires. Some rigid objects or rigid object groups may be further constrained to translate or rotate in specified directions, if the design requires.  
         [0035]     The method may be extended to handle situations where objects are required to maintain certain properties. In the case of rigid objects, the property in question is shape. But other examples of properties might be volume or distance to another object or contact with another object. The set of all objects with a given property is called an admissible set. A member of an admissible set is called an admissible object. In a deformation scenario, an object which is to maintain or achieve a given property is called a pre-admissible object. In the extended method, a pre-admissible object is deformed under a warp. Then, the element of the admissible set that is closest or approximately closest (in terms of the aforementioned properties) to the deformed pre-admissible object is computed. Then, a new warp is computed, using as an additional origin/destination modifier pair the pre-admissible object and the element of the admissible set that is closest to the deformed pre-admissible object. This new warp is applied to the non-pre-admissible objects, while the pre-admissible object is replaced by its corresponding admissible object. This method can be used, for example, to cause a curve or object to move along another curve (like curtain rings along a curved curtain rod), or cause a curve or object to maintain a constant distance from another curve that is being deformed (such as the two edges of a ribbon) while otherwise following a given deformation. Meanwhile the non-pre-admissible objects are deformed in a manner that seamlessly matches the deformations of the pre-admissible objects. The concept of finding a closest point in an admissible set is familiar from the field of geometric numerical integration, where the state of a mechanical system (e.g. a double pendulum) must be kept within a configuration space (see, for example, Section IV.4 of “Geometric Numerical Integration” by E. Hairer, C. Lubich, G. Wanner, Springer-Verlag, 2002.)  
         [0036]     Additional details of the derived transformations will be discussed later herein.  
         [0037]     Another problem with the deformation of the entire space is that while the interpolation/approximation handles positional data, it does not handle differential data. In particular, conventional methods do not give a way of “holding” surface normals (i.e. tangent planes) at constraints. This is a problem because constraints usually define the boundary of a deformation, and the user will usually require that the deformed portion of the model blend smoothly with the (undeformed) remainder of the model. This is depicted in  FIGS. 7 and 8 .  FIG. 7  depicts a setup similar to that in  FIG. 1 . In  FIG. 8  the deformation has been applied. As can be seen, the surface orientation along the constraint lines has changed (i.e. the surface normals have changed direction). See also  FIGS. 27-31  for another example.  
         [0038]     A solution to this problem is to provide tangent continuous deformations. In this solution a secondary scalar spatial function—called the “fade” function is computed. It has a value of: “1” on modifiers; “0” on constraints where tangent continuity is to be preserved; “1” on remaining constraints. An interpolation/approximation is computed over all space, using methods similar to those for the deformation (e.g. radial basis functions or hierarchical volume splines).  
         [0039]     When the deformation is evaluated at a point, it is multiplied by the fade function at that point. It can be shown mathematically that the resultant deformation has no effect on normals on the designated constraints—this is basically due to the product rule in elementary differential calculus: (fg)′=f′g+fg′=f′ 0 +0g′=0, where f and g are the fade and deformation functions respectively. In  FIG. 9  the deformation in  FIG. 7  has been applied. The constraint  902  on the right is a tangential constraint. As can be seen the surface orientation along constraint  902  is the same as prior to the deformation.  
         [0040]     In a preferred implementation, the interpolation of the fade function should be as “linear” as possible. For example, if you are using radial basis functions, the basis functions should be linear. If you are using volume splines, the splines should be linear.  
         [0041]     The scheme can be “tweaked” to get other boundary transition behaviors such curvature continuity and order-n continuity.  
         [0042]     Additional details of the tangent continuous constraint transformations will be discussed later herein.  
         [0043]     Another problem with the deformation of the entire model is that irregularities (non-smoothness) in the defining data can lead to wild interpolations.  FIG. 10  illustrates a flat mesh  1002  to be deformed with positional constraints  1004  and  1006  on the left and right, and origin  1008  and destination  1010  modifier curves are in the middle. The arrow  1012  points to a point constraint that constrains the mesh to not move at that point. The point constraint was inadvertently selected by the user, and gives a directive that strongly clashes with the intended deformation. The irregular data can result from user error (such as inadvertently picking constraints, or specifying contradictory modifiers), noisy data, or other reasons.  FIG. 11  depicts the wildly fluctuating mesh surface  1102  caused in the region of deformation to the left of the constraint  1106 . The deformation is rather violent, and not what the user expected. The user needs a way of diagnosing which data points are leading to violent behavior in the interpolation and, optionally, automatically culling irregular data points.  
         [0044]     A solution to this problem is to provide Laplacian point culling. (A Laplacian is generally defined as the difference between a quantity and an average of its neighboring quantities.) Given a discrete vector field (i.e. a finite set of points with attached vectors), we find a measure of the “smoothness” of this data. Should any data points deviate too much from their neighbors, these data points should be culled.  
         [0045]     Let i=0, 1, 2 . . . , n−1 index the sample points. Let d i  be the vector corresponding to sample i, and let r ij  be the distance between samples i and j. Then the point set Laplacian for sample i is defined as:  
           ∑     i   ≠   j       ⁢           ⁢       (       d   i     -     d   j       )     ⁢     /     ⁢     r   ij   2             ∑     i   ≠   j       ⁢           ⁢     1     r   ij             
 
         [0046]     This expression measures the deviation of a vector from a weighted average of all of the other vectors. The weighting gives nearer neighbors a greater weight than farther neighbors. The measure is scale independent, meaning that it does not change if the samples and vectors are uniformly scaled. If the size of the Laplacian is large, then there is a significant “bump” or discrepancy in the data that may lead to an unwieldy interpolation.  
         [0047]     Computing the Laplacian for the deformation vector at every sample point solves the given problem. Sample points with Laplacians with a length over a given threshold (in our implementation we use 2.0) can either be highlighted, or automatically culled. In fact, points can be colored with a color range that indicates where they are on the continuum between “safe” and “problematic”.  FIG. 12  illustrates the deformation defined in  FIG. 10 , after the offending sample has been automatically culled.  
         [0048]     Additional details of the Laplacian culling will be described later herein.  
         [0049]     The embodiments discussed herein operate within and as part of a conventional computer system as shown in  FIG. 13  executing a modeling package such as AliasStudio® available from Autodesk. Such a system includes a computer  1302  that executes the processes discussed herein at the direction of a user using a keyboard  1304  and mouse  1306  and displays the results on a display  1308 .  
         [0050]     In performing a deformation using a modifier, the user often recognizes that anomalies such as those discussed above occur. In such a situation the user can select a solution to the anomaly from among the set of solutions discussed above. This solution is then applied during the deformation process to fix the anomaly. The set of solutions is discussed in more detail below.  
         [0000]     Region Clamp Embodiment  
         [0051]      FIG. 14  starts another example of the clamping function and shows a mesh surface  1402  with modifier curves  1403  and  1404  and a positional constraint curve  1406 . As can be seen, the constraint curve  1406  is not a closed curve and has a break  1408 . As depicted in  FIG. 15 , when the modifier curves  1503  and  1504  are lifted to their deforming position, the entire surface  1502 , inside (respectively outside) the positional constraint curve  1506  is pulled up (respectively down). When clamping is activated, as depicted in  FIG. 16 , the surface  1602  outside the constraint is clamped to the original level even though the level of the surface at the modifier is pulled up. Because the clamping region is calculated via interpolation, the break  1608  is effectively closed.  
         [0052]     Sometimes the region determined by automatic clamping does not extend to all areas that the user would like to be unaffected by the deformation. This limit on the clamping region can result in anomalous behavior that can also be solved with a clamper point.  FIG. 17  depicts a simple surface  1702  and an associated constraint  1704  and a modifier  1706 . When the modifier  1806  is allowed to modify the surface  1802  without clamping, the surface  1802  is deformed as in  FIG. 18 . When the clamping is turned on, because the clamping region of effect of the curve  1904  is limited (see  FIG. 19 ), the surface  1902  shows the range or limit  1908  of the clamping region  1910 . When this occurs, as depicted in  FIG. 20 , a clamper point  2012  can be inserted in the middle of the clamp region. This additional clamping information is enough to extend the computed clamp region to include the entire left end of the mesh  2002 . The user can insert this clamper  2012  when the user recognizes the anomaly. As an alternative, this determination of the location of the insertion point could be automatic, as described later herein.  
         [0053]     The clamping operation, as depicted in  FIG. 21  starts with inputting  2102  the target surface, the modifier, the constraint and the clamper geometry. The system then samples  2104  the modifier, constraint and the clamper geometry. Next, the system assigns  2106  modifier samples a value of 1, constraint samples a value of 0 and clamper samples a value of −1. The system next interpolates  2108  between the assigned values. The deformation function is then computed  2110  followed by the determination  2112  of the deformation at a specific point. If more points need to be computed  2114 , the system loops back. If not, the system is finished  2116 .  
         [0054]     The transfer function, m(t), for the clamping limited deformation is depicted in  FIG. 22  and zero on one side  2202  of the constraint  2204  and one on the other side  2206 .  
         [0055]     In the above-discussed process, for a point x, we calculate the raw deformation vector g(x) and the scalar f(x). The value of the final deformation vector is m(f(x))g(x).  
         [0056]     As discussed above, both f( ) and g( ) are calculated by interpolation of values set at sample points. In the following table, the sample point types are across, and the modification types, including those to be discussed later, are down. The values given in the table are the values that are interpolated by f( ).  
                                                                                     Tangent   Positional               Modifier   Constraint   Constraint   Clamper                                    Clamp   1   0   0   −1       Tangent   1   0   1   n/a       Continuous and       Order-n       Continuous                  
 
         [0057]     In the foregoing, we use the sign of the clamping function to determine whether a point is to be clamped or not. That is, the clamping function determines the clamping region. It is a common in algorithms to define regions in this way, i.e. as implicit surfaces and regions. Not only is membership in a region determined by a simple function evaluation, but also this function evaluation may be much faster than an algorithm that works through geometric calculations. On the other hand, the clamping region determined as in  FIG. 21  may not meet user expectations as well as a region determined by other means such as sophisticated geometric calculations or user inspection. But we can encode such an improved region by supplementing the points to be interpolated by the clamping function so that the new clamping region matches the improved region to within reasonable tolerance. An example of this is the use of clamper points supplied by the user. (For a reference that explains how to encode a region using implicit functions, see “Modeling with Implicit Surfaces that Interpolate”, Greg Turk and James F. O&#39;Brien, ACM Transactions on Graphics, Vol. 21, No 4, October 2002 at http://www.cc.gatech.edu/˜turk/my_papers/vimp tog.pdf)  
         [0000]     Rigid Deformation Embodiment  
         [0058]     To illustrate the operations associated with deformations of models that include rigid objects, we start by depicting, in  FIG. 23 , a surface  2302  to be deformed by a modifier  2304  that will move the surface toward the modifier and where the surface  2302  includes rigid rings or grommets  2306 . When the deformation is performed, the grommets  2406  are stretched along with the surface  2402  as depicted in  FIG. 24 . When the rigid deformation of this embodiment that accounts for the movement of the rigid objects is performed, the grommets  2506  are moved relative to the deformation of the surface  2502  to keep their shape as shown in  FIG. 25 .  
         [0059]     The rigid deformation operations start with inputting  2602  the constraints, modifiers, flexible targets and rigid targets. Based on the modifiers, constraints, and targets, the system generates  2604  a warp A of the flexible surface. This warp A is generated and applied  2606  to the rigid targets. Once this warp is applied, the motion of the rigid targets is extracted  2608 . The motion of the rigid objects is used to generate  2610  a warp B using the motion of the rigid objects as additional modifiers. The warp B is then applied  2612  to the flexible targets and results in deformation of the surface without the deformation of the rigid objects.  
         [0000]     Tangent Continuity and Order-n Continuity Embodiment  
         [0060]     To help visualize the problem of not maintaining tangent continuity and effect of doing so, the discussion below will use a diagnostic stripe pattern reflected from the surface being deformed. In industrial and automotive design applications, reflections are often used to evaluate higher order continuity properties of surfaces. For example, a positional reflection discontinuity corresponds to a tangential surface discontinuity, and a tangential reflection discontinuity corresponds to a discontinuity in surface curvature.  FIG. 27A  depicts a perspective view of a surface  2702  reflecting a zebra stripe pattern. This surface  2702  has associated with it a constraint curve  2704  and a modifier  2706 .  FIG. 27B  provides a side view. When the surface  2802  (see  FIGS. 28A  &amp; B) is deformed toward the modifier  2806  without clamping at the constraint curve  2804 , the reflection has maintained its regular appearance with no discontinuities in the reflected stripes. When automatic clamping is turned on, as depicted in  FIGS. 29A  &amp; B, the surface on one side of the constraint maintains its position while the surface on the other side is deformed. As can be seen, the stripe pattern reflected on the surface  2902  shows reflection discontinuities at the constraint curve  2904 . When a tangent continuity function that applies a tangent constraint to the surface  3002  is applied in association with the constraint curve  3004 , the reflection discontinuities are removed as depicted in  FIGS. 30A and 30B . However, the reflection still has artifacts that may be unwanted, such as the noticeable change of direction of the stripes that makes the transition particularly visible. When order-n continuity (for n=2) is also applied, as depicted in  FIGS. 31A  &amp; B, to provide a second order tangent continuity, the stripes have no discontinuities and do not change direction at the constraint. This sort of smooth transition is desirable in, for example, the automotive industry. Note that, when n=1, order-n continuity is the same as tangent continuity.  
         [0061]     The process performed for this embodiment, starts with inputting  3202  ( FIG. 32 ) the target surface, the modifier, the positional constraint and the tangent constraint geometry. The system then samples  3204  the modifier, positional constraint and the tangent constraint geometry. Next, the system assigns  3206  modifier and positional constraint samples a value of 1, and tangent constraint samples a value of 0. The system next interpolates  3208  between the assigned values. The deformation function is then computed  3210 , followed by the determination  3212  of the deformation at a specific point. If more points need to be computed  3214 , the system loops back. If not, the system is finished  3216 .  
         [0062]     The transfer function, m(t), for the tangent continuous limited deformation is depicted in  FIG. 33  and is zero at the constraint (t=0), less than zero on one side of the constraint (t&lt;0) and greater than zero on the other side (t&gt;0).  
         [0063]     The transfer function, m n (t), for the order-n continuous limited deformation is depicted in  FIG. 34  and is less than zero and accelerating downward on one side of the constraint and greater than zero and accelerating upward on the other side, while the first n−1 derivatives vanish at the constraint. Note that, when n=1, the function m n (t) is the same as m(t).  
         [0064]     When clamping is applied, the values of the tangent continuous and order-n continuous transfer functions m(t) and m n (t) for values of t&lt;0 are irrelevant, because clamping is applied for those values. Alternatively if the values of m(t) and m n (t) are defined as zero for t&lt;0, then clamping and tangent/order-n continuity can be applied in a single step, even though they are conceptually different.  
         [0000]     Laplacian Culling Embodiment  
         [0065]      FIG. 35  shows an original setup where a surface or plane  3502  is to be deformed. The two lines  3504  and  3506  are a modifier pair (indicating that the warp must translate points on the lower line to the upper line). There s also short constraint line or curve  3508  approximately perpendicular to the lower modifier (indicating that points along that line must not move). Where the constraint  3508  and lower modifier  3504  intersect there is a deformation contradiction (the point should move but it should remain unmoved). Generally in performing a deformation, however, each line is sampled and it is unlikely that the intersection point will be a sample. So generally, there will be nearby (as opposed to identical samples) points that have nearly contradictory deformation instructions (i.e. one sample point moves, but another very close sample point does not move). Generally, such contradictions are accidental—they are not what the user intends.  FIG. 36  shows the anomalous results of a deformation based on the modifiers and constraint of  FIG. 35 .  FIG. 37  illustrates the deformation after Laplacian culling is performed.  
         [0066]     The process (see  FIG. 38 ) performed for this embodiment starts by inputting  3802  a list of sample points and associated vectors. A variable threshold is also input and is used to remove points from the list. The system then determines  3804  the Laplacian of a point on the list in accordance with the equation discussed previously. If the Laplacian is above the threshold, the point is removed  3806  from the list. If a point is removed from the list  3808 , the system goes back and checks for other points that are outliers. When no more points are removed, the system is finished  3810  and the deformation can be performed.  
         [0067]     The techniques taught herein are described in three dimensions, but they are applicable in any number of dimensions. In the two dimensional case they could be applied, for example, to image processing, where the need also exists to control image deformations in the ways described herein. The techniques taught herein are described with respect to modifying the shapes of surfaces, but are also applicable to other geometries such as curves and point clouds, and objects in arbitrary dimensions.  
         [0068]     The many features and advantages of the invention are apparent from the detailed specification and, thus, it is intended by the appended claims to cover all such features and advantages of the invention that fall within the true spirit and scope of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and accordingly all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.