CN117726710A - Curve dispersion-based drawing method and related device - Google Patents
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Abstract
The application relates to the field of numerical control processing and image drawing, in particular to a drawing method and a related device based on curve dispersion, wherein the method comprises the steps of obtaining a NURBS curve for representing the geometric form of an object to be drawn, and dividing the NURBS curve into a plurality of Bezier curves; determining a discrete parameter set of the NURBS curve based on the control vertex set of each Bezier curve; traversing discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn; drawing the object to be drawn based on the discrete point set. According to the method and the device, the NURBS curve is divided into the plurality of Bezier curves, the discrete parameter set is determined through the control polygon of the Bezier curve, the non-uniform characteristic of the NURBS curve and the curve part with large curvature change are reserved, the matching degree of the discrete point set and the object to be drawn is improved, and the accuracy of drawing the image can be improved.
Description
Technical Field
The application relates to the technical field of numerical control machining and image drawing, in particular to a drawing method based on curve dispersion and a related device.
Background
When numerical control machining or drawing is performed in CAD drawing, object data of an object to be drawn is obtained first, and then an object drawing is made according to the object data. Many objects to be drawn are characterized by curves, such as the center trajectory of a tool, the curves of an aircraft wing, etc. When drawing a drawing image corresponding to an object to be drawn, a curve for representing the object to be drawn needs to be discretized, and then drawing is performed based on a discrete point set obtained by discretization.
The NURBS (non-uniform rational B-spline) curve is widely used to construct complex geometries by virtue of its own good properties. However, existing NURBS discretization methods generally employ a uniform parameter discretization method that discretizes NURBS curves by uniformly selecting a set of parameter values in the parameter domain of the NURBS curve. Although the NURBS curve can be discretized, for a curve with non-uniform characteristics or large curvature change, the curve detail and the bending part cannot be well expressed, so that the NURBS curve discretization is lack of precision, the matching degree of a drawing image drawn based on a discretized point set and an image to be drawn is influenced, the image precision of the drawing image obtained by drawing is influenced, and further, a processing object displayed or processed based on the drawing image cannot meet the requirement.
Disclosure of Invention
The technical problem to be solved by the application is to provide a drawing method based on curve dispersion and a related device aiming at the defects of the prior art.
In order to solve the above technical problems, a first aspect of an embodiment of the present application provides a method for drawing based on curve dispersion, where the method includes:
acquiring a NURBS curve for representing the geometric form of an object to be drawn, and dividing the NURBS curve into a plurality of Bezier curves;
determining a discrete parameter set of the NURBS curve in a cumulative chord length mode based on a control vertex set of each Bezier curve;
traversing discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn;
and drawing the object to be drawn based on the discrete point set to obtain a drawing image corresponding to the object to be drawn.
The curve dispersion-based drawing method, wherein the dividing the NURBS curve into a plurality of bezier curves specifically includes:
the NURBS curve is refined into a plurality of first Bezier curves in a node inserting mode, and each first Bezier curve is used as a target Bezier curve;
Obtaining the control polygon type of each target Bezier curve;
and performing halving segmentation on each target Bezier curve according to the control polygon type of each target Bezier curve so as to obtain a plurality of Bezier curves.
The curve dispersion-based drawing method is characterized in that the control polygon type comprises a convex type and a concave type; the performing binary segmentation on each target Bezier curve according to the control polygon type of each target Bezier curve to obtain a plurality of Bezier curves specifically comprises:
for a target Bezier curve with a control polygon type of a convex type, taking the target Bezier curve as a Bezier curve obtained by dividing the NURBS curve;
for a target Bezier curve with a concave control polygon type, performing halving segmentation on the target Bezier curve to obtain two second Bezier curves;
and taking the two second Bezier curves as target Bezier curves, and re-acquiring the control polygon type of each target Bezier curve.
The curve dispersion-based drawing method, wherein the re-obtaining the control polygon type of each target bezier curve by taking the two second bezier curves as the target bezier curves specifically includes:
Taking the two second Bezier curves as target Bezier curves, and obtaining the dividing times of the first Bezier curves to which the target Bezier curves belong;
and when the dividing times are smaller than the preset times, re-acquiring the control polygon types of the target Bezier curves.
The curve dispersion-based drawing method, wherein the re-acquiring the control polygon type of each target bezier curve by taking the two second bezier curves as the target bezier curves further includes:
and when the dividing times are greater than or equal to the preset times, discarding target curve points in the target Bezier curves, and re-acquiring the control polygon types of the target Bezier curves, wherein the target curve points are curve points with zero curvature in the target Bezier curves.
The curve dispersion-based drawing method, wherein the determining the dispersion parameter set of the NURBS curve by the cumulative chord length method based on the control vertex set of each bezier curve specifically comprises:
for each segment of Bezier curve, selecting an initial control vertex of the Bezier curve;
for each non-initial control vertex of the Bezier curve, acquiring the string vector length between the non-initial control vertex and the previous control vertex, and calculating the temporary discrete parameters of the non-initial control vertex according to the string vector length and the temporary discrete parameters of the previous control vertex to obtain a temporary discrete parameter set of the Bezier curve;
Converting the temporary discrete parameter set into a parameter domain corresponding to the Bezier curve to obtain a target discrete parameter set corresponding to the Bezier curve;
and taking the union set of target discrete parameter sets corresponding to all Bezier curves as the discrete parameter set of the NURBS curve.
The drawing method based on curve dispersion, wherein the dispersing each discrete parameter interval to obtain the discrete point set corresponding to the object to be drawn specifically includes:
for each discrete parameter interval, taking the discrete parameter interval as a target discrete parameter interval;
acquiring the number of times of Bezier curves corresponding to the target discrete parameter interval;
generating a reference Bezier curve based on the target discrete parameter interval and the times, and acquiring curve characteristics of the reference Bezier curve;
if the curve characteristics meet preset conditions, taking points corresponding to the upper limit parameter, the lower limit parameter and the middle parameter of the target discrete parameter interval on a Bezier curve as discrete points corresponding to the NURBS curve;
if the curve characteristics do not meet preset conditions, dividing the discrete parameter interval into two sub-discrete parameter intervals, taking each sub-discrete parameter interval as a target discrete parameter interval, and generating a reference Bezier curve again based on the target discrete parameter interval and the times to obtain discrete points corresponding to the NURBS curve;
And taking all the discrete points as the discrete points of the NURBS curve to obtain a discrete point set corresponding to the object to be drawn.
The curve dispersion-based drawing method is characterized in that the curve characteristics comprise one or more of bow height, chord length and tangent vector included angle, wherein the tangent vector included angle is an included angle of a tangent vector taking a curve point corresponding to the middle parameter of the discrete parameter interval as a tangent point and a tangent vector taking a curve point corresponding to the upper limit parameter of the discrete parameter interval as a tangent point.
The method for drawing based on curve dispersion, wherein after the drawing is performed on the object to be drawn based on the discrete point set to obtain a drawing image corresponding to the object to be drawn, the method further comprises:
and performing a downstream operation on the drawn image, wherein the downstream operation comprises one or more of displaying the drawn image, outputting the drawn image to a processing device, outputting the drawn image from a simulation model, and outputting the drawn image to a sampling device.
A second aspect of the embodiments of the present application provides a drawing device based on curve dispersion, the device including:
the acquisition module is used for acquiring NURBS curves used for representing the geometric form of the object to be drawn and dividing the NURBS curves into a plurality of Bezier curves;
The determining module is used for determining a discrete parameter set of the NURBS curve in a cumulative chord length mode based on the control vertex set of each Bezier curve;
the discrete module is used for traversing the discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn;
and the drawing model is used for drawing the object to be drawn based on the discrete point set so as to obtain a drawing image corresponding to the object to be drawn.
A third aspect of the embodiments provides a computer-readable storage medium storing one or more programs executable by one or more processors to implement steps in a curve dispersion based rendering method as described in any of the above.
A fourth aspect of the present embodiment provides a terminal device, including: a processor and a memory;
the memory has stored thereon a computer readable program executable by the processor;
the processor, when executing the computer readable program, implements the steps in the curve dispersion based rendering method as described in any one of the above.
The beneficial effects are that: compared with the prior art, the application provides a drawing method based on curve dispersion and a related device, wherein the method comprises the steps of obtaining a NURBS curve for representing the geometric form of an object to be drawn, and dividing the NURBS curve into a plurality of Bezier curves; determining a discrete parameter set of the NURBS curve by a cumulative chord length mode based on the control vertex set of each Bezier curve; traversing discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn; drawing the object to be drawn based on the discrete point set. According to the method and the device, the NURBS curve is divided into the plurality of Bezier curves, the discrete parameter set is determined through the control polygon of the Bezier curve, the non-uniform characteristic of the NURBS curve and the curve part with large curvature change are reserved, the matching degree of the drawing image and the object to be drawn is improved, the accuracy of the drawing image can be improved, and the accuracy of the drawing object based on the processing or display of the drawing image can be further ensured.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is an exemplary graph of NURBS curves.
Fig. 2 is a flowchart of a curve dispersion-based drawing method provided in the present application.
Fig. 3 is a flowchart of one example of a curve dispersion-based rendering method provided in the present application.
Fig. 4 is an exemplary graph of NURBS curves.
Fig. 5 is a schematic diagram of the NURBS curve shown in fig. 4 divided into several bezier curves.
Fig. 6 is a schematic diagram of a bezier curve for controlling the polygon type to be a concave type.
Fig. 7 is a schematic diagram of a cumulative chord mode process.
Fig. 8 is a schematic representation of a discrete point set obtained by the discretization of the NURBS curve shown in fig. 4.
Fig. 9 is a schematic structural diagram of a drawing device based on curve dispersion provided in the present application.
Fig. 10 is a schematic structural diagram of a terminal device provided in the present application.
Detailed Description
The present application provides a drawing method based on curve dispersion and a related device, and in order to make the purposes, technical solutions and effects of the present application clearer and more definite, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or wirelessly coupled. The term "and/or" as used herein includes all or any element and all combination of one or more of the associated listed items.
It will be understood by those skilled in the art that all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs unless defined otherwise. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
It should be understood that the sequence number and the size of each step in this embodiment do not mean the sequence of execution, and the execution sequence of each process is determined by the function and the internal logic of each process, and should not constitute any limitation on the implementation process of the embodiment of the present application.
According to research, when numerical control machining or drawing is performed in CAD drawing, object data of an object to be drawn is obtained first, and then an object drawing is made according to the object data. Many objects to be drawn are characterized by curves, such as the center trajectory of a tool, the curves of an aircraft wing, etc. When drawing a drawing image corresponding to an object to be drawn, a curve for representing the object to be drawn needs to be discretized, and then drawing is performed based on a discrete point set obtained by discretization.
The NURBS (non-uniform rational B-spline) curve is widely used to construct complex geometries by virtue of its own good properties. However, existing NURBS discretization methods generally employ a uniform parameter discretization method that discretizes NURBS curves by uniformly selecting a set of parameter values in the parameter domain of the NURBS curve. Although the method can discretize the NURBS curve, for the curve with non-uniform characteristics or large curvature variation (for example, the NURBS curve shown in fig. 1), curve details and curved parts cannot be well expressed, so that the NURBS curve discretization has a lack of precision, which influences the matching degree of a drawing image drawn based on a discretized discrete point set and an image to be drawn, thereby influencing the image precision of the drawing image obtained by drawing, and further, the processing object processed based on the drawing image cannot meet the production requirement or the display requirement when displayed based on the drawing image.
In order to solve the above problem, in the embodiment of the present application, NURBS curves for characterizing the geometric form of an object to be drawn are acquired, and the NURBS curves are divided into several bezier curves; determining a discrete parameter set of the NURBS curve by a cumulative chord length mode based on the control vertex set of each Bezier curve; traversing discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn; drawing the object to be drawn based on the discrete point set. According to the method and the device, the NURBS curve is divided into the plurality of Bezier curves, the discrete parameter set is determined through the control polygon of the Bezier curve, the non-uniform characteristic of the NURBS curve and the curve part with large curvature change are reserved, the matching degree of the drawing image and the object to be drawn is improved, the accuracy of the drawing image can be improved, and the accuracy of the drawing object based on the processing or display of the drawing image can be further ensured.
The application will be further described by the description of embodiments with reference to the accompanying drawings.
The embodiment provides a drawing method based on curve dispersion, and relates to the technical fields of numerical control machining and image drawing. For example, the curve bar of the aircraft wing is represented by using a NURBS curve, the appearance of the wing is analyzed and simulated in the aircraft design process, or the NURBS curve of the aircraft wing used for representation needs to be discretized in the manufacturing process, and the like, so as to obtain a discrete point set corresponding to the object to be drawn, and then the aircraft wing is analyzed, simulated or processed based on the discrete point set corresponding to the NURBS curve, so that a smooth aircraft wing model is obtained. According to the embodiment of the application, the accuracy of the discrete point set of the NURBS curve is improved by improving the discrete method of the NURBS curve, the discretization of the NURBS curve for representing the aircraft wing by adopting the drawing method based on curve dispersion provided by the embodiment of the application can be improved, and the accuracy of the aircraft wing obtained by drawing can be improved.
As shown in fig. 2, the drawing method based on curve dispersion provided in the embodiment of the present application specifically includes:
S10, acquiring NURBS curves used for representing the geometric form of the object to be drawn, and dividing the NURBS curves into a plurality of Bezier curves.
Specifically, the object to be drawn may be an object to be processed, an object to be simulated, or the like in the numerical control processing field, or may be an object to be drawn in the image drawing field, where the object to be drawn may be characterized by adopting a NURBS curveThe geometric form of the tool is that an object to be drawn is an airplane wing, and the object to be drawn is a tool center track. The NURBS curve may be represented by several control vertices and their corresponding weights, e.g., givenControl vertex->And its corresponding weight->The NURBS curve can be expressed as:
，
wherein,representing control vertex->Representing the weight factor->Representing a +.>sub-B spline basis function, only node vector +.>It will have an influence on the same,each node vector in (1) has a size of 0,1]。
Bezier curves are typically defined by control vertices that determine the geometry of the curve. The start control vertex and the end control vertex of the curve are part of the control vertex, and the shape of the curve is determined by the position and weight of the control vertex. In the embodiment of the application, the control vertex of the NURBS curve for characterizing the geometry of the object to be drawn may be determined according to the shape of the object to be drawn. For example, a starting point and an ending point of an object to be drawn and a bending point in the object to be drawn are selected according to the shape of the object to be drawn, all the selected points are ordered according to the direction from the starting point to the ending point, and for each two adjacent points, control vertices between the two adjacent points are calculated according to a preset Bezier curve order, so that a control vertex set corresponding to the object to be drawn is obtained.
In the embodiment of the application, the NURBS curve is divided into a plurality of sections of bezier curves, each section of bezier curve in the plurality of bezier curves is a part of the NURBS curve, wherein the plurality of bezier curves can be directly obtained through node vectors inserted in the NURBS curve, or can be obtained by inserting new node vectors in the NURBS curve to obtain a plurality of first bezier curves, and then performing halving division according to the control polygon type of the bezier curve.
In one implementation of the present application, as shown in fig. 3, the splitting the NURBS curve into several bezier curves specifically includes:
s11, refining the NURBS curve into a plurality of first Bezier curves by inserting nodes, and taking each first Bezier curve as a target Bezier curve;
s12, obtaining the control polygon type of each target Bezier curve;
s13, performing halving segmentation on each target Bezier curve according to the control polygon type of each target Bezier curve so as to obtain a plurality of Bezier curves.
In particular, refining the NURBS curve by inserting nodes refers to the original parameter set of the NURBS curveNew parameter values are inserted and then a new set of control vertices is calculated from the inserted set of parameter sets. That is, before the NURBS curve is refined into a plurality of first bezier curves by inserting nodes, the values of parameters to be inserted corresponding to the NURBS curve need to be obtained, wherein The parameter values to be inserted may be preset.
To further illustrate the refinement of NURBS curves, we useThe sub NURBS curves are illustrated as examples. As shown in FIG. 4, for a given +.>subNURBS curve->，/>Control vertex set of +.>The weight factor set is->The node vector is +.>，/>，/>Is the control vertex maximum subscript of NURBS curve, to be inserted parameter set +.>For all->The method comprises the following steps: />，Calculate a new set of control vertices +.>The calculation formulas of the weighted control vertexes and the weight factors of the new control vertex set are respectively as follows:
，
wherein,controlling vertex set for original weighting before inserting node,/->A product set for multiplying each coordinate of the control vertex with the corresponding weight; />Is the original control right factor set; />And->Respectively a new weighted control vertex set and a new weighted control weight factor set after node insertion; />Is an intermediate coefficient factor.
And sequentially inserting the insertion nodes in the parameter value set to be inserted into the original parameter set according to the process, so as to obtain a curve shown in fig. 5. Furthermore, it is worth noting that, for example, the insertion node in the parameter value set to be inserted isAnd2 times and 3 times, then +.>Requiring sequential insertion.
In step S12, since the bezier curve is defined by a series of control vertices, the control vertices used to define the bezier curve may form a polygon that is a control polygon of the bezier curve, wherein the control polygon type may be determined by the positions of the control vertices included in the control polygon. Accordingly, the control polygon type may be determined according to the positions of the control vertices included in the control polygon, for example, the internal angles included in the control polygon are determined according to the positions of the control vertices included in the control polygon, and then the control polygon type is determined according to all the internal angles, or alternatively, the sides of the control polygon are determined according to the positions of the control vertices included in the control polygon, and then the control polygon type is determined according to the positional relationship of all the sides, and so on.
In this embodiment, the control polygon type is determined according to all the internal angles included in the control polygon, the convex type refers to all the internal angles included in the control polygon being smaller than 180 degrees, and the concave type refers to at least one internal angle existing in all the internal angles included in the control polygon being larger than 180 degrees. Therefore, when the control polygon type of each target bezier curve is acquired, the angle values of all the internal angles inside the control polygon of the target bezier curve can be acquired, and when all the acquired angle values are smaller than 180 degrees, the control polygon is indicated to be of a convex type, whereas when at least one angle value is larger than 180 degrees, the control polygon is indicated to be of a concave type.
In step S13, after the control polygon type is obtained, the target bezier curves may be divided into two halves according to the control polygon type, where when the control polygon type is a convex type, it is indicated that there are no feature points in the target bezier curves that affect the dispersion of the curves, for example, points with zero curvature, such as points or inflection points, and where the curves are knotted; conversely, when the control polygon type is a concave type, it is explained that there are characteristic points in the target bezier curve that affect the dispersion of the curve, for example, a curve as shown in fig. 6. Therefore, for a target bezier curve with a control polygon type being a convex type, the target bezier curve can be directly segmented as a bezier curve obtained by NURBS curve segmentation, and for a target bezier curve with a control polygon type being a concave type, a special point in the target bezier curve can be directly removed, the removed target bezier curve can be directly segmented as a bezier curve obtained by NURBS curve segmentation, and the target bezier curve can be segmented again, so that the control polygon type of the target bezier curve obtained by subdivision again is a convex type.
In an implementation manner of the embodiment of the present application, as shown in fig. 3, the performing, according to the control polygon type of each target bezier curve, binary segmentation on each target bezier curve to obtain a plurality of bezier curves specifically includes:
s131, regarding a target Bezier curve with a control polygon type being a convex type, taking the target Bezier curve as a Bezier curve obtained by dividing the NURBS curve;
s132, for a target Bezier curve with a concave control polygon type, performing halving division on the target Bezier curve to obtain two second Bezier curves, taking the two second Bezier curves as target Bezier curves, and re-acquiring the control polygon type of each target Bezier curve.
Specifically, the halving of the target Bezier curve refers to taking intermediate parameters within the defined domain of the target Bezier curveAnd calculates the intermediate parameter +.>Point +.>Then go through the dot->The target bezier curve is divided into two second bezier curves, wherein the control vertex of each second bezier curve can be obtained simultaneously when the decussate-teryle recursion algorithm is executed, and the following description can be referred to specifically.
In the embodiment of the application, the target Bezier curve with the concave control polygon type is converted into the Bezier curve with the convex control polygon type by subdividing the target Bezier curve again, so that control vertexes can be reserved as much as possible, geometric features of the NURBS curve can be reserved as much as possible, and the accuracy of a discrete point set obtained by subsequent discrete can be improved.
Further, a dead cycle occurs in order to re-execute the step of acquiring the control polygon type of each target bezier curve, or the curve dispersion speed is affected because the number of times of re-executing the step of acquiring the control polygon type of each target bezier curve is excessive. In this embodiment of the present application, an end condition is set for the step of re-executing the control polygon type of obtaining each target bezier curve, where the end condition may be that all the control polygon types of the bezier curves obtained by segmentation are convex types, or the end condition may be that one of a preset condition 1 and a preset condition 2 is met, the preset condition 1 is that all the control polygon types of the bezier curves obtained by segmentation are convex types, and the preset condition 2 is that the number of times of segmentation of the first bezier curve to which the bezier curve whose control polygon type is concave reaches a preset number of times. In this embodiment of the present application, the end condition is one of the preset condition 1 and the preset condition 2, so that on one hand, the segmentation can be avoided from entering the dead cycle, and on the other hand, the discrete efficiency can be ensured by controlling the segmentation times.
Based on this, the re-acquiring the control polygon types of each target bezier curve by using the two second bezier curves as the target bezier curves specifically includes:
s1331, taking the two second Bezier curves as target Bezier curves, and obtaining the segmentation times of a first Bezier curve to which the target Bezier curves belong;
s1332, when the segmentation times are smaller than preset times, the control polygon types of the target Bezier curves are acquired again.
Specifically, the preset number of times is preset, and is used for balancing the discrete efficiency and the basis of reserving the geometric characteristics of the NURBS curve by the bezier curve, for example, the preset number of times is 2,3, and the like. In this embodiment, the preset number of times is 3, and the control polygon of each bezier curve after 3 times of binary segmentation may approximately represent the geometric feature of the bezier curve. In addition, in practical application, there may be a case that the number of divisions is greater than or equal to a preset number of divisions, and when the number of divisions is greater than or equal to the preset number of divisions, the step of directly executing the control vertex set based on each bessel curve and determining the discrete parameter set of the NURBS curve by accumulating the chord length method may also be performed on the target bessel curve, so that the control polygon type of the processed target bessel curve is a convex type. Therefore, the control polygon types of all the partitioned Bezier curves are convex, and the accuracy of determining the discrete point set based on the partitioned Bezier curves can be improved.
Based on this, in the embodiment of the present application, taking the two second bezier curves as the target bezier curves, the reacquiring the control polygon types of the target bezier curves further includes:
s1333, when the dividing times are larger than or equal to the preset times, discarding the target curve points in the target Bezier curves, and re-acquiring the control polygon types of the target Bezier curves.
Specifically, the target curve point is a curve point with a curvature of zero in the target bezier curve, and by discarding the curve point with a curvature of zero in the target bezier curve, curve points with a corresponding control polygon type of concave type caused by inflection points and the like in the target bezier curve can be removed, so that the control polygon types of all the divided bezier curves can be made to be convex type.
S20, determining a discrete parameter set of the NURBS curve in a cumulative chord length mode based on the control vertex set of each Bezier curve.
Specifically, the discrete parameter set includes a plurality of discrete parameters, the plurality of discrete parameters are determined from a control vertex set of the Bezier curve, and the plurality of discrete parametersOne-to-one correspondence with control vertices in the control vertex set, and a plurality of discrete parameters are positioned on the same straight line. That is, each control vertex is mapped onto a connection line of a starting control vertex and a ending control vertex along the curve extending direction in the control vertex set in a cumulative chord length mode, so as to obtain discrete parameters corresponding to each control vertex. For example, as shown in FIG. 7, the control vertices of the control polygon of the Bezier curve are aggregated into The discrete parameter set determined by means of cumulative chord length is +.>。
In one implementation manner of the embodiment of the present application, the determining, by means of cumulative chord length, the discrete parameter set of the NURBS curve based on the control vertex set of each bezier curve specifically includes:
s21, selecting an initial control vertex of each segment of Bezier curve;
s22, for each non-initial control vertex of the Bezier curve, acquiring the string vector length between the non-initial control vertex and the previous control vertex, and calculating the temporary discrete parameters of the non-initial control vertex according to the string vector length and the temporary discrete parameters of the previous control vertex to obtain a temporary discrete parameter set of the Bezier curve;
s23, converting the temporary discrete parameter set into a parameter domain corresponding to the Bezier curve to obtain a target discrete parameter set corresponding to the Bezier curve;
s24, taking the union set of target discrete parameter sets corresponding to all Bezier curves as the discrete parameter set of the NURBS curve.
Specifically, the Bezier curve includesEach control vertex corresponds to a temporary discrete parameter which is a numerical value, wherein the numerical value corresponding to each control vertex can And determining by the value of the temporary discrete parameter corresponding to the 0 th control vertex. In this embodiment of the present application, the temporary discrete parameter corresponding to the 0 th control vertex (initial control vertex) is set to 0, the temporary discrete parameters corresponding to other non-initial control vertices are set to values greater than 0, and the value of the previous temporary discrete parameter in the temporary discrete parameters corresponding to the two adjacent non-initial control vertices is smaller than the value of the next temporary discrete parameter.
The string vector length refers to the previous control vertexAnd the current control vertex +.>Formed string vector +.>Wherein the string vector +.>The calculation formula of (2) is +.>The string vector length can be expressed as +.>. Based on this, the Bezier curve comprises +.>The respective temporary discrete parameters for each of the control vertices may be expressed as:
；
；
wherein,representing the correspondence of the 0 th control vertexTemporary discrete parameter->Indicate->Temporary discrete parameters corresponding to the control vertices, +.>Indicate->Temporary discrete parameters corresponding to the control vertices, +.>Express->String vector length corresponding to each control vertex, +.>The maximum subscript of the control point representing NURBS.
Further, after the temporary discrete parameters corresponding to each control vertex are obtained, in order to map each temporary discrete parameter to the parameter domain of the bezier curve, domain transformation may be performed on the obtained temporary discrete parameter set, so as to obtain a target discrete parameter set located in the parameter domain. The process of performing domain transformation on the temporary discrete parameter set can be expressed as follows:
，
Wherein,parameter field representing Bezier curve, +.>Indicate->Control verticesCorresponding temporary discrete parameters->Indicate->And the temporary discrete parameters corresponding to the control vertexes.
S30, traversing the discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn.
Specifically, the discrete point set includes a plurality of data points, and a curve formed by connecting the plurality of data points is used as a discrete representation of an object to be drawn, wherein each data point corresponds to one object point in the object to be drawn. That is, the discrete point set includes data points corresponding to a plurality of object points in the object to be drawn, and when the data points are sequentially drawn, a drawing image corresponding to the image to be drawn can be drawn. For example, the object to be drawn is an aircraft wing, each data point in the discrete point set corresponds to a corresponding position point of a wing shape on the aircraft wing, and the position relationship between adjacent data points is consistent with the position point relationship of the corresponding wing shape, so that the aircraft wing graph can be drawn according to the discrete point set.
The discrete parameter set comprises a plurality of discrete parameters, the discrete parameters are arranged in order from small to large to form a discrete parameter sequence, and any two adjacent discrete parameters in the discrete parameter sequence form a discrete parameter interval. The curve part corresponding to each discrete parameter interval is used as a point set part to be discrete, the discrete points corresponding to the point set part to be discrete are obtained by dispersing the discrete parameter interval, then the discrete points corresponding to all the point set parts to be discrete form a discrete point set of the NURBS curve, for example, the NURBS curve shown in figure 4 is subjected to discrete to obtain the discrete point set shown in figure 8.
In an implementation manner of the embodiment of the present application, the dispersing each discrete parameter interval to obtain the discrete point set corresponding to the object to be drawn specifically includes:
s31, regarding each discrete parameter interval, taking the discrete parameter interval as a target discrete parameter interval;
s32, acquiring the number of times of Bezier curves corresponding to the target discrete parameter interval;
s33, generating a reference Bezier curve based on the target discrete parameter interval and the times, and acquiring curve characteristics of the reference Bezier curve;
S34, if the curve characteristics meet preset conditions, taking points corresponding to the upper limit parameter, the lower limit parameter and the intermediate parameter of the target discrete parameter interval on a Bezier curve as discrete points corresponding to the NURBS curve, wherein the intermediate parameter is equal to the average value of the upper limit parameter and the lower limit parameter;
s35, if the curve characteristics do not meet preset conditions, dividing the discrete parameter interval into two sub-discrete parameter intervals, taking each sub-discrete parameter interval as a target discrete parameter interval, and generating a reference Bezier curve again based on the target discrete parameter interval and the times to obtain discrete points corresponding to the NURBS curve;
s36, taking all the discrete points as the discrete points of the NURBS curve to obtain a discrete point set corresponding to the object to be drawn.
In particular, the discrete parameter set is expressed as，/>Indicate->Discrete parameters->Representing the number of discrete parameters, the discrete parameter interval may represent +.>，/>The number of times of the Bezier curve may be equal to the number of times of the NURBS curve, e.g. the number of times of the Bezier curve is +.>And twice. The reference Bezier curve is given by the initial parameter +.>Ending parameter->And the number of times of Bezier curves to which the discrete parameter interval belongs +. >As an input, the calculation is obtained through a decussate recursion algorithm, wherein the calculation process and the control vertex of the decussate recursion algorithm can be expressed as:
;
;
wherein,representing the number of recursive steps,/->Representing control vertex->Curve points on the Bessel curve, < >>，/>Representing Bernstein basis functions, +.>Representing the initial control vertex.
Further, the curved features include one or more of a height of the bow, a chord length, and a tangent vector angle, for example, the curved features include a height of the bow, a chord length, or a height of the bow and a tangent vector angle, or a height of the bow, a chord length, and a tangent vector angle, etc. In practical applications, where only bow height is used to control segmentation, NURBS curves with excessive local curvature variations may still not capture their detail or non-uniformity. Thus, in embodiments of the present application, the curve features include bow height, chord length, and tangent vector angle, where bow height is the starting parameterAnd ending parameter->Intermediate parameters of->Point +.>To the initial parameters->Point on the point set segment to be discretized corresponding to the discretized parameter interval +.>And ending parameter->Point on the point set segment to be discretized corresponding to the discretized parameter interval +. >Is used for the distance of the connecting line of the pair of the electronic device. The chord length is the initial parameter->Point on the point set segment to be discretized corresponding to the discretized parameter interval +.>And ending parameter->Points on the point set segment to be discretized corresponding to the discretized parameter intervalThe distance between the two edges of the tangential vector included angle are curve points corresponding to the intermediate parameters of the discrete parameter intervalTangent vector as tangent point and curve point corresponding to upper limit parameter of discrete parameter interval +.>Is the tangent vector of the tangent point.
Further, the preset condition is preset and is an iteration ending condition for limiting the discrete parameter interval segmentation, wherein the preset condition is determined according to curve characteristics, and when the curve characteristics comprise bow height, chord length and tangent vector included angle, the preset condition is that the bow height is smaller than a preset bow height threshold value, the chord length is smaller than a preset chord length threshold value and the tangent vector included angle is smaller than an angle tolerance. That is, when the target discrete parameter interval determination curve characteristic satisfies the preset condition, the upper limit parameter, the lower limit parameter, and the intermediate parameter of the target discrete parameter interval are maintained; and when the curve characteristic is determined to not meet the preset condition by the target discrete parameter interval, circularly executing to take each sub-discrete parameter interval as the target discrete parameter interval, and generating a reference Bezier curve again based on the target discrete parameter interval and the times to obtain the discrete points corresponding to the NURBS curve until the curve characteristic meets the preset condition or the times of segmentation reach the preset threshold value to obtain a discrete point set.
And S40, drawing the object to be drawn based on the discrete point set so as to obtain a drawing image corresponding to the object to be drawn.
Specifically, after the discrete point set is obtained, the discrete characterization (i.e., the discrete point set) of the object to be drawn is adopted to obtain drawing of the object to be drawn, so as to obtain a drawing image. That is, after the discrete point set is acquired, each data point in the discrete point set is sequentially drawn, and when all the data points are drawn, the obtained image is a drawing image corresponding to the object to be drawn. Further, after the drawing image is obtained, a downstream operation may be performed based on the drawing image, wherein the downstream operation may be a process path for constructing an object to be drawn, or may be displaying the drawing image or the like. In an implementation manner of the embodiment of the present application, after the drawing the object to be drawn based on the discrete point set to obtain a drawing image corresponding to the object to be drawn, the method further includes:
and performing a downstream operation on the drawn image, wherein the downstream operation comprises one or more of displaying the drawn image, outputting the drawn image to a processing device, outputting the drawn image from a simulation model, and outputting the drawn image to a sampling device.
In summary, the present embodiment provides a drawing method based on curve dispersion, which is based on a drawing method of curve dispersion and a related device, the method includes obtaining a NURBS curve for characterizing a geometric form of an object to be drawn, and dividing the NURBS curve into a plurality of bezier curves; determining a discrete parameter set of the NURBS curve by a cumulative chord length mode based on the control vertex set of each Bezier curve; traversing discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn; drawing the object to be drawn based on the discrete point set. According to the method and the device, the NURBS curve is divided into the plurality of Bezier curves, the discrete parameter set is determined through the control polygon of the Bezier curve, the non-uniform characteristic of the NURBS curve and the curve part with large curvature change are reserved, the matching degree of the drawing image and the object to be drawn is improved, the accuracy of the drawing image can be improved, and the accuracy of the drawing object based on the processing or display of the drawing image can be further ensured.
Based on the above-mentioned drawing method based on curve dispersion, the present embodiment provides a drawing device based on curve dispersion, as shown in fig. 9, the device includes:
An acquisition module 100, configured to acquire a NURBS curve for characterizing a geometric form of an object to be drawn, and divide the NURBS curve into a plurality of bezier curves;
a determining module 200, configured to determine a discrete parameter set of the NURBS curve by means of cumulative chord length based on the control vertex set of each bezier curve;
the discrete module 300 is configured to traverse discrete parameter intervals in the discrete parameter set, and discrete each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn;
and the drawing model 400 is used for drawing the object to be drawn based on the discrete point set so as to obtain a drawing image corresponding to the object to be drawn.
Based on the above-described curve dispersion-based drawing method, the present embodiment provides a computer-readable storage medium storing one or more programs executable by one or more processors to implement the steps in the curve dispersion-based drawing method as described in the above-described embodiment.
Based on the curve dispersion-based drawing method, the application also provides a terminal device, as shown in fig. 10, which includes at least one processor (processor) 20; a display screen 21; and a memory (memory) 22, which may also include a communication interface (Communications Interface) 23 and a bus 24. Wherein the processor 20, the display 21, the memory 22 and the communication interface 23 may communicate with each other via a bus 24. The display screen 21 is configured to display a user guidance interface preset in the initial setting mode. The communication interface 23 may transmit information. The processor 20 may invoke logic instructions in the memory 22 to perform the methods of the embodiments described above.
Further, the logic instructions in the memory 22 described above may be implemented in the form of software functional units and stored in a computer readable storage medium when sold or used as a stand alone product.
The memory 22, as a computer readable storage medium, may be configured to store a software program, a computer executable program, such as program instructions or modules corresponding to the methods in the embodiments of the present disclosure. The processor 20 performs functional applications and data processing, i.e. implements the methods of the embodiments described above, by running software programs, instructions or modules stored in the memory 22.
The memory 22 may include a storage program area that may store an operating system, at least one application program required for functions, and a storage data area; the storage data area may store data created according to the use of the terminal device, etc. In addition, the memory 22 may include high-speed random access memory, and may also include nonvolatile memory. For example, a plurality of media capable of storing program codes such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or a transitory storage medium may be used.
In addition, the specific processes that the storage medium and the plurality of instruction processors in the terminal device load and execute are described in detail in the above method, and are not stated here.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and are not limiting thereof; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (12)
1. A method of curve dispersion based rendering, the method comprising:
acquiring a NURBS curve for representing the geometric form of an object to be drawn, and dividing the NURBS curve into a plurality of Bezier curves;
determining a discrete parameter set of the NURBS curve in a cumulative chord length mode based on a control vertex set of each Bezier curve;
traversing the discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn;
And drawing the object to be drawn based on the discrete point set to obtain a drawing image corresponding to the object to be drawn.
2. The curve dispersion based drawing method according to claim 1, wherein the dividing the NURBS curve into a plurality of bezier curves specifically comprises:
the NURBS curve is refined into a plurality of first Bezier curves in a node inserting mode, and each first Bezier curve is used as a target Bezier curve;
obtaining the control polygon type of each target Bezier curve;
and performing halving segmentation on each target Bezier curve according to the control polygon type of each target Bezier curve so as to obtain a plurality of Bezier curves.
3. The curve dispersion based drawing method according to claim 2, wherein the control polygon type includes a convex type and a concave type; the performing binary segmentation on each target Bezier curve according to the control polygon type of each target Bezier curve to obtain a plurality of Bezier curves specifically comprises:
for a target Bezier curve with a control polygon type of a convex type, taking the target Bezier curve as a Bezier curve obtained by dividing the NURBS curve;
And for the target Bezier curves with concave control polygon types, performing halving segmentation on the target Bezier curves to obtain two second Bezier curves, taking the two second Bezier curves as target Bezier curves, and re-acquiring the control polygon types of the target Bezier curves.
4. The curve dispersion based drawing method according to claim 3, wherein the re-acquiring the control polygon type of each target bezier curve by using the two second bezier curves as target bezier curves specifically includes:
taking the two second Bezier curves as target Bezier curves, and obtaining the dividing times of the first Bezier curves to which the target Bezier curves belong;
and when the dividing times are smaller than the preset times, re-acquiring the control polygon types of the target Bezier curves.
5. The curve dispersion based drawing method according to claim 4, wherein the re-acquiring the control polygon type of each target bezier curve with the two second bezier curves as target bezier curves further includes:
and when the dividing times are greater than or equal to the preset times, discarding target curve points in the target Bezier curves, and re-acquiring the control polygon types of the target Bezier curves, wherein the target curve points are curve points with zero curvature in the target Bezier curves.
6. The curve discrete-based drawing method according to claim 1, wherein the determining the discrete parameter set of the NURBS curve by means of the cumulative chord length based on the control vertex set of each bezier curve specifically comprises:
for each segment of Bezier curve, selecting an initial control vertex of the Bezier curve;
for each non-initial control vertex of the Bezier curve, acquiring the string vector length between the non-initial control vertex and the previous control vertex, and calculating the temporary discrete parameters of the non-initial control vertex according to the string vector length and the temporary discrete parameters of the previous control vertex to obtain a temporary discrete parameter set of the Bezier curve;
converting the temporary discrete parameter set into a parameter domain corresponding to the Bezier curve to obtain a target discrete parameter set corresponding to the Bezier curve;
and taking the union set of target discrete parameter sets corresponding to all Bezier curves as the discrete parameter set of the NURBS curve.
7. The method for drawing based on curve dispersion according to claim 1, wherein the dispersing each discrete parameter interval to obtain the discrete point set corresponding to the object to be drawn specifically includes:
For each discrete parameter interval, taking the discrete parameter interval as a target discrete parameter interval;
acquiring the number of times of Bezier curves corresponding to the target discrete parameter interval;
generating a reference Bezier curve based on the target discrete parameter interval and the times, and acquiring curve characteristics of the reference Bezier curve;
if the curve characteristics meet preset conditions, taking points corresponding to the upper limit parameter, the lower limit parameter and the middle parameter of the target discrete parameter interval on a Bezier curve as discrete points corresponding to the NURBS curve;
if the curve characteristics do not meet preset conditions, dividing the discrete parameter interval into two sub-discrete parameter intervals, taking each sub-discrete parameter interval as a target discrete parameter interval, and generating a reference Bezier curve again based on the target discrete parameter interval and the times to obtain discrete points corresponding to the NURBS curve;
and taking all the discrete points as the discrete points of the NURBS curve to obtain a discrete point set corresponding to the object to be drawn.
8. The method of claim 7, wherein the curve features include one or more of bow height, chord length, and tangent vector angle, wherein the tangent vector angle is an angle of tangent vector having a curve point corresponding to an intermediate parameter of the discrete parameter interval as a tangent point and a tangent vector having a curve point corresponding to an upper limit parameter of the discrete parameter interval as a tangent point.
9. The method for drawing an object to be drawn based on curve dispersion according to claim 1, wherein after the drawing the object to be drawn based on the set of discrete points to obtain a drawing image corresponding to the object to be drawn, the method further comprises:
and performing a downstream operation on the drawn image, wherein the downstream operation includes one or more of displaying the drawn image, outputting the drawn image to a device, and outputting a simulation model to the drawn image.
10. A curve dispersion based rendering device, the device comprising:
the acquisition module is used for acquiring NURBS curves used for representing the geometric form of the object to be drawn and dividing the NURBS curves into a plurality of Bezier curves;
the determining module is used for determining a discrete parameter set of the NURBS curve in a cumulative chord length mode based on the control vertex set of each Bezier curve;
the discrete module is used for traversing the discrete parameter intervals in the discrete parameter set, and dispersing each discrete parameter interval to obtain a discrete point set corresponding to the object to be drawn;
and the drawing model is used for drawing the object to be drawn based on the discrete point set so as to obtain a drawing image corresponding to the object to be drawn.
11. A computer readable storage medium storing one or more programs executable by one or more processors to implement the steps in the curve dispersion based rendering method of any one of claims 1-9.
12. A terminal device, comprising: a processor and a memory;
the memory has stored thereon a computer readable program executable by the processor;
the processor, when executing the computer readable program, implements the steps of the curve dispersion based rendering method according to any one of claims 1-9.
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