CN106981095B - A kind of improved smooth free-form deformation - Google Patents
A kind of improved smooth free-form deformation Download PDFInfo
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Abstract
The invention discloses a kind of improved smooth Free Transform algorithms, belong to computer image processing technology field, the algorithm includes the uniform subdivision step of triangle, in the uniform subdivision step of triangle, by utilizing equal segments length control parameters, the side length for making subdivision generate sub- triangle effectively prevents the generation of long-narrow triangular mesh or degeneration triangle close to equal segments length control parameters, keeps smooth Free Transform more robust efficiently.
Description
Technical field
The present invention relates to computer image processing technology fields, specifically, being related to a kind of improved smooth Free Transform
Algorithm.
Background technique
In Geometric Modeling and computer animation, geometric distortion is the key that geometric shape editor and flexible body animation producing
One of technology, wherein most representative is Free Transform technology (FFD), and multiple mutation have been developed, such as accurate Free Transform
Method, smooth free-form deformation etc., since its is easy to use, powerful, have been integrated into 3DS Max, Maya,
In the business softwares such as Softimage XSI.
Since the deformation of traditional free-form deformation is applied on the sampled point of model to be edited, then by sampling point deformation
Position recovering afterwards goes out the deformation result of model, causes it to exist in deformation process and loses shape because sampling point density is too small
The problem of.
To solve the problems, such as to lose shape, usually increase the density of sampled point, but will cause biggish expense in performance；More into one
The method of step is adaptively to determine sampling density according to patch-sized and curvature of curved surface, adaptive although reducing performance cost
It answers algorithm to realize relative complex, and some singularities can not be handled well.
Accurate Free Transform is by cutting initial triangle along node box as the method for solving the problems, such as to lose shape in FFD
Dough sheet calculates enough deformed positions of number sampled point on tri patch, then calculates original triangular facet with sampling-point interpolation
The deformed precise results of piece.
Smooth free-form deformation improves accurate free-form deformation by following six step:
(1) deformation space step is defined
It selects B-spline body as deformation space, is denoted as R (μ, ν, ω):
Wherein,Indicate mμ×mν×mωA control vertex, It is B-spline basic function.
Then model to be deformed is wrapped up with the deformation space.
(2) triangulation step
Divide initial tri patch by the node box on B-spline body.
(3) model insertion step
In this step, telescopiny is to calculate the process of model parameter coordinate in deformation space to be deformed, specific logical
It crosses imbedding function U=E (X) and sampled point is mapped to deformation space from world coordinate system, wherein X is sampled point in world coordinates
Coordinate in system, U are parameter coordinate of the sampled point in deformation space.
Imbedding function E is determined by deformation space, in smooth Free Transform, usually passes through certain method construct B-spline
Body keeps the parameter coordinate of embedding distortion spatial point equal with coordinate of this in world coordinate system, i.e. E (X)=X, with simplification
Calculating in telescopiny.
And usually select three times bezier surface piece be fitted accurate deformation result, due to each cutting generate three
It is angular, a triangle Bayside patch can be all obtained after deformation, so the triangle to generate in each cutting is enterprising
Row sampling, needs 3 × 3 obligatory points and m (m is determined by the number of deformation space) a match point altogether, i.e., smooth Free Transform is total
Need 9+m sampled point.
Then parameter coordinate of the sampled point in deformation space is calculated with E (X)=X, while passes through barycentric coodinates interpolation
Calculate the normal direction of sampled point.
(4) geometry deformation step
Geometry deformation process is to change deformation space and the process by the displacement transfer to model to be deformed, will specially be adopted
Sampling point be embedded in B-spline body in, with by these sampled points by the displacement transfer of deformation space into model to be deformed.Work as user
Behind the position for changing B-spline body control vertex, the parameter coordinate of sampled point and control vertex position are first updated to definition deformation
In formula used in space, in the hope of the deformed position of sampled point；It is again input with these new positions, passes through belt restraining
Approximating method finds out the control vertex of the triangle bezier surface as deformation result.
(5) normal deformation step
In order to solve the problems, such as that result is not smooth natural enough in accurate Free Transform, must adopt by barycentric coodinates interpolating estimation
The normal direction of sampling point, the normal vector for then calculating sampled point deform later value；Then, with identical with geometry deformation step
Method is input with the deformed normal vector of sampled point, fits deformed triangular surface piece with bezier surface piece three times
Normal vector field.In subdivision stage while close classification vector field, and in this, as the normal direction of subdivision triangle, to can be obtained in light
Slide two sides visually G1Continuous geometry and G0Continuous normal vector field；In sharp edge two sides G0Continuous geometry and G-1Continuously
Normal vector field.
(6) geometry trim step
Visually finer and smoother deformation result in order to obtain is also needed according to normal direction information to the three tooth shell plugs for indicating geometry
You are finely adjusted the control vertex of patch.
(7) plot step is segmented
It is drawn after normal deformation step is finely divided with the result in geometry trim step.
After the processing of above-mentioned seven steps, by the way that CUDA to be applied in accurate Free Transform, can not only it realize
50 times faster than accurate free-form deformation or so of calculating speed, and improve the visual attractiveness of deformation result.But
In the uniform subdivision step of triangle, triangle is cut along node box, has the following problems: (1) being easy to be cut into long-narrow triangular mesh
With degeneration triangle, computing resource can be not only wasted, can may also bring floating number to calculate mistake, program operation speed is caused to become
Slowly, robustness is deteriorated；(2) triangle of usually cutting generation is smaller, and deformed error is also smaller, but in this step, cuts
The triangle size being cut into determines that user is difficult to control cutting result, that is, can not by the distribution of node box and model Triangle-Profile
The size of error after model deformation is controlled.
Summary of the invention
It is an object of the present invention to provide a kind of improved smooth Free Transform algorithms, are calculated with solving existing smooth Free Transform
The problem of method intermediate cam subdivision step, so that smooth Free Transform is more robust efficiently.
To achieve the goals above, smooth Free Transform algorithm provided by the invention includes the uniform subdivision step of triangle；Three
The uniform subdivision step in angle includes:
Step 1, initial tri patch is obtained；
Step 2, according to equal segments length control parameters, equal part is carried out to the both sides of initial tri patch Minimum Internal Angle；
Step 3, two Along ents for connecting neighbouring Minimum Internal Angle vertex form ventral triangle shape and to subdivision quadrangle；
Step 4, it using the endpoint shared to subdivision quadrangle and ventral triangle shape as starting point, is correspondingly connected on subdivision quadrangle
Along ent, it is trapezoidal to be split into several classes；
Step 5, according to equal segments length control parameters, equal part is carried out to the trapezoidal top margin of class and bottom edge, and connect Along ent
Carry out triangulation trapezoidal to class；If the equal part points on Minimum Internal Angle both sides differ, repeatedly step 4 and step 5, with distance
The farthest class in Minimum Internal Angle vertex is trapezoidal to carry out triangulation to subdivision quadrangle, and be located at Minimum Internal Angle etc. point points compared with
Vertex on few side is starting point.
In the uniform subdivision step of above-mentioned triangle, using equal segments length control parameters, the sub- triangle for generating cutting
Side length close to equal segments length control parameters, that is, the sub- triangle for dividing generation is closer to equilateral triangle, effectively prevents narrow
The generation of Yangtze River Delta shape or degeneration triangle keeps smooth Free Transform process more robust efficiently.
It includes: according to equal part that one specific scheme, which is the step of carrying out etc. dividing according to equal segments length control parameters opposite side,
Number of segment opposite side carries out equal part, and equal part number of segment is the value that rounds up of the quotient of edge lengths and equal segments length control parameters.Algorithm letter
It is single.
Another concrete scheme is that step 2 includes: to receive the setting of reciprocity section length control parameter.It is used by receiving
The setting of family equity section length control parameter, the size for generating sub- triangle to segmentation convenient for user controls, with basis
The performance of demand and hardware, controls distortion inaccuracy.
Another concrete scheme is that step 2 includes: to calculate Minimum Internal Angle both sides according to the apex coordinate of initial tri patch
Length；The equal part number of segment on Minimum Internal Angle both sides is calculated, equal part number of segment is the quotient's of edge lengths and equal segments length control parameters
Round up value；According to the extreme coordinates on both sides, the coordinate of Along ent is calculated.
Another specific scheme, step 1 include: that model to be deformed is read from file；It treats distorted pattern and carries out three
Angling forms initial tri patch.
Another specific scheme, step 2 include: to calculate each edge lengths, most according to the apex coordinate of initial tri patch
Small interior angle is the interior angle opposite with most short side.
The step of another specific scheme, connection Along ent trapezoidal to class progress triangulation includes: along same connection
Direction, connection the trapezoidal upper bottom of class with go to the bottom on correspond to Along ent, form several quadrangles, and connect short diagonal to quadrangle into
Row subdivision.
Preferred scheme be further include step 6: subdivision result is optimized using CVT optimization method.Segmentation can be made to tie
Fruit is more uniform.
Further preferred embodiment carries out 5 CVT optimization to subdivision result.Effect of optimization is better balanced to open with calculating
Pin.
Compared with the existing methods, the beneficial effects of the present invention are:
(1) do not include plane in algorithm and ask friendship, more efficiently, robust.
(2) the sub- triangle that subdivision goes out is close to equilateral triangle and area is close to equal, will not generate new long and narrow or degeneration
Triangle.
Detailed description of the invention
Fig. 1 is the work flow diagram of the embodiment of the present invention；
Fig. 2 is the work flow diagram of the uniform subdivision step of intermediate cam of the embodiment of the present invention；
Fig. 3 is the partial routine schematic diagram of the uniform subdivision step of intermediate cam of the embodiment of the present invention, wherein (a) is initial three
Edged surface piece (b) is the Minimum Internal Angle for finding out initial tri patch, (d) is to cut open (c) to carry out equal part to Minimum Internal Angle both sides
The ventral triangle shape separated, it is (e) trapezoidal for first class to subdivision, (f) equal part is carried out for upper bottom trapezoidal to first class.
Fig. 4 is the other parts process schematic of the uniform subdivision step of intermediate cam of the embodiment of the present invention, and (a) is to first
The trapezoidal carry out triangulation of class (b) is that the class ladder of subdivision (c) is waited for for the last one to the trapezoidal carry out triangulation of second class
Shape (d) is progresss part trapezoidal to the last one class triangulation, (e) be triangulation as a result, (f) be to subdivision result into
Row CVT optimization.
Specific embodiment
With reference to embodiments and its attached drawing the invention will be further described.
Embodiment
Referring to Fig. 1, the improved smooth Free Transform algorithm of the present invention is uniformly cutd open including definition deformation space step S1, triangle
S2, model insertion step S3, geometry deformation step S4, normal deformation step S5, geometry trim step S6 and subdivision are drawn step by step
Step S7 processed.
Deformation space step S1 is defined, defines a B-spline body as the deformation space for wrapping up model to be deformed.
The uniform subdivision step S2 of triangle is divided the initial tri patch in model to be deformed with the uniform subdivision algorithm of triangle
At several sub- triangles, with the error after Reducing distortion.
Referring to fig. 2, the uniform subdivision step S2 of triangle include obtaining step S21, etc. step by step S22, connection Along ent step
S23, subdivision quadrangle step S24, subdivision class trapezoidal step S25 and Optimization Steps S26.
Obtaining step S21 obtains initial tri patch.
Model to be deformed is read from file；
It treats distorted pattern and carries out trigonometric ratio, form the initial tri patch 1 as shown in Fig. 3 (a).
Deng S22 step by step, according to equal segments length control parameters l, the both sides of initial tri patch Minimum Internal Angle are carried out
Equal part.
The setting of reciprocity section length control parameter l is received, user is according to initial tri patch size and its to precision
It is required that setting control parameter l by input interface, allow users to preferably control distortion inaccuracy.
As shown in Fig. 3 (b), according to the apex coordinate of initial tri patch 1, calculate its while 11, while 12 and side 13 length
Degree, then using ranking method to three edge lengths carry out ascending order arrangement, wherein be located at primary side 13 pair angle α be initial three
The Minimum Internal Angle of edged surface piece 1.
Calculate Minimum Internal Angle while 11 with while 12 length；According to equal segments length control parameters l, calculate while 11 with while 12
Equal part number of segment, wherein equal part number of segment is the value that rounds up of the quotient of edge lengths and equal segments length control parameters l, i.e. side 11
Equal part number of segment with side 12 is respectivelyWhereinFor the length on side 11,For the length on side 12.
According to while 11 with while 12 extreme coordinates, calculate Along ent coordinate, one side specific for Minimum Internal Angle, such as side
11, if the coordinate of two endpoint is P1, P2, thenFor the coordinate of each Along ent on side 11, wherein n is
Equal part number of segment, the value of t are 0 to n.Equal part is carried out to the both sides 11,12 of the Minimum Internal Angle of initial tri patch 1, as a result as schemed
Shown in 3 (c).
Along ent step S23 is connected, referring to Fig. 3 (d), two Along ents on neighbouring Minimum Internal Angle vertex is connected, forms top
Triangle 2 with to subdivision quadrangle 3.
Subdivision quadrangle step S24, as shown in Fig. 3 (d), with the endpoint shared to subdivision quadrangle 3 and ventral triangle shape 2
It for starting point, is correspondingly connected with to the Along ent on subdivision quadrangle 3, is split into that several classes are trapezoidal, such as the bold portion of Fig. 3 (e)
For first class trapezoidal 31.
The trapezoidal step S25 of subdivision class, by taking first class trapezoidal 31 as shown in Fig. 3 (e) as an example, foundation etc. divides segment length control
Parameter l processed, upper bottom and bottom to first class trapezoidal 31 carry out equal part, as a result as shown in Fig. 3 (f)；Along same connection direction,
For example by the from left to right in figure, upper bottom will be correspondingly connected with and cutd open with the quadrangle that Along ent is formed of going to the bottom with its short diagonal
Point, as a result as shown in Fig. 4 (a).
From top to bottom, sequentially carry out triangulation trapezoidal to each class, during subdivision, as shown in Fig. 4 (b), second
Bottom is equal with the equal part number of segment of bottom in a class trapezoidal 32, is connected thereto on bottom and bottom and corresponds to Along ent, forms several four sides
Shape calculates its two cornerwise length according to the four of quadrangle vertex, divides quadrangle along that shorter diagonal line,
Each quadrangle is finally set to be divided into two triangles.
As shown in Fig. 4 (c), the upper bottom segmentation number of segment of third class trapezoidal 33 is fewer by 1 than going to the bottom, and divides equally to upper bottom and bottom
Point is numbered, and the number at upper bottom is from left to right 1 to k, and the number of bottom is from left to right 1 to k+1, trapezoidal in third class
On 33, first identical point is numbered in bottom in connection.In addition to this, for each point in upper bottom, if its number is j, make by
It is connected with the point that number is j+1 in bottom, and third class trapezoidal 33 is finally divided into multiple jagged triangles.
If the equal part points on Minimum Internal Angle both sides differ, as shown in Fig. 4 (c), Fig. 4 (d), step S24 and step are repeated
S25, with the class trapezoidal 34 farthest apart from Minimum Internal Angle vertex to carry out triangulation to subdivision quadrangle, and to be located in minimum
Vertex on the less side of angle etc. point points is starting point.By the class trapezoidal 33 farthest apart from Minimum Internal Angle vertex rotation 90 counterclockwise
Degree keeps such trapezoidal 33 similar to subdivision quadrangle 3 in Fig. 3, extends such trapezoidal 33 upper bottom and bottom, after intersection and most
The remainder of the another a line of small interior angle constitutes a triangle, the triangle as the original triangle as shown in Fig. 3 (a)
Dough sheet, and step S22 to step S25 is executed to it, in subdivision process, initial tri patch 1 is divided into as shown in Fig. 4 (d),
Until tri patch 1 is split into as shown in Fig. 4 (e).
Optimization Steps S26 carries out initial 1 subdivision result of tri patch using CVT optimization method as shown in Fig. 4 (f)
Optimization, and 5 CVT optimization is carried out to the result, keep sub- triangle more uniform.CVT optimization method be DU Q, FABER V,
GUNZBURGER M.CentroidalVoronoi tessellations: applications and algorithms[J]
.SIAM review, 1999,41 (4): the method introduced in 637-676.
Model insertion deformation space is calculated the sampling of each tri patch generated after subdivision by model insertion step S3
Parameter coordinate and normal direction of the point in deformation space.
Geometry deformation step S4, user change the control vertex of deformation space, deform to deformation space.Keep sampling
Point parameter coordinate in deformation space is constant, new position of the sampled point under world coordinate system is calculated, after obtaining deformation
Sampled point, it is deformed as a result, the result triangle Bezier to calculate each tri patch with the approximating method of belt restraining
Patch indicates.
Normal deformation step S5 calculates new normal direction of the sampled point under world coordinate system, according to obtaining deformed adopt
The normal direction of sampling point calculates the deformed normal vector field of each tri patch, the result triangle with the approximating method of belt restraining
Bezier surface piece indicates.
Geometry trim step S6, the control vertex for the triangle bezier surface piece that adjustment geometry deformation step S4 is obtained, makes
The more smooth nature of deformation result.
Plot step S7 is segmented, is drawn after the result in normal deformation step S5 and geometry trim step S6 is finely divided
System.
Claims (9)
1. a kind of improved smooth free-form deformation, including definition deformation space step, the uniform subdivision step of triangle, model are embedding
Enter step, geometry deformation step, normal deformation step, geometry trim step and subdivision plot step, which is characterized in that described three
The uniform subdivision step in angle is realized in GPU platform, comprising:
Step 1, initial tri patch is obtained；
Step 2, according to equal segments length control parameters, equal part is carried out to the both sides of initial tri patch Minimum Internal Angle；
Step 3, two Along ents for connecting neighbouring Minimum Internal Angle vertex form ventral triangle shape and to subdivision quadrangle；
Step 4, using the endpoint shared to subdivision quadrangle and ventral triangle shape as starting point, be correspondingly connected on subdivision quadrangle etc.
It is trapezoidal to be split into several classes for branch；
Step 5, equal part is carried out according to the equal segments length control parameters, upper bottom trapezoidal to class and bottom, and connects Along ent
Carry out triangulation trapezoidal to class；If the equal part points on Minimum Internal Angle both sides differ, repeatedly step 4 and step 5, with distance
The farthest class in Minimum Internal Angle vertex is trapezoidal to carry out triangulation to subdivision quadrangle, and be located at Minimum Internal Angle etc. point points compared with
Vertex on few side is starting point.
2. smooth free-form deformation according to claim 1, which is characterized in that according to equal segments length control parameters pair
While carry out etc. include: the step of dividing
According to etc. divide number of segment opposite side to carry out equal part, equal part number of segment be the quotient of edge lengths and the equal segments length control parameters to
Upper rounding value.
3. smooth free-form deformation according to claim 1, which is characterized in that the step 2 includes:
Receive the setting to the equal segments length control parameters.
4. smooth free-form deformation according to claim 1, which is characterized in that the step 2 includes:
According to the apex coordinate of initial tri patch, the length on Minimum Internal Angle both sides is calculated；
The equal part number of segment on Minimum Internal Angle both sides is calculated, equal part number of segment is the quotient's of edge lengths and the equal segments length control parameters
Round up value；
According to the extreme coordinates on both sides, the coordinate of Along ent is calculated.
5. smooth free-form deformation according to claim 1, which is characterized in that the step 1 includes:
Model to be deformed is read from file；
It treats distorted pattern and carries out trigonometric ratio, form initial tri patch.
6. smooth free-form deformation according to claim 1, which is characterized in that the step 2 includes:
According to the apex coordinate of initial tri patch, each edge lengths are calculated, Minimum Internal Angle is the interior angle opposite with most short side.
7. smooth free-form deformation according to claim 1, which is characterized in that the connection Along ent it is trapezoidal to class into
The step of row triangulation includes:
Along same connection direction, connect the trapezoidal upper bottom of class with go to the bottom on correspond to Along ent, form several quadrangles, and connect it is short right
Linea angulata carries out subdivision to quadrangle.
8. according to claim 1 to smooth free-form deformation described in any one of 7 claims, which is characterized in that further include:
Step 6, subdivision result is optimized using CVT optimization method.
9. smooth free-form deformation according to claim 8, it is characterised in that:
5 CVT optimization is carried out to subdivision result.
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| CN110570504B (en) * | 2019-09-06 | 2020-12-01 | 北京航天宏图信息技术股份有限公司 | Closed symbol drawing method and device, electronic equipment and storage medium |
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