CN107248163B - Automatic generation method of texture development diagram for rotationally symmetric porcelain - Google Patents
Automatic generation method of texture development diagram for rotationally symmetric porcelain Download PDFInfo
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Abstract
The invention discloses an automatic generation method of a pattern development diagram facing a rotational symmetry porcelain, which comprises the following steps: inputting data information of a model with two-dimensional textures; secondly, obtaining an upright model based on the symmetry axis rotation model, and further obtaining front views of the upright model in front, back, left and right directions; analyzing the four obtained front views by using a gradient operator to generate a cumulative gradient map of the model; step four, calculating a model cutting plane on the basis of the obtained cumulative gradient map to complete the segmented processing of the model; step five, performing circular truncated cone fitting on each obtained segmented model; step six, judging whether a non-textured special area exists in the fitting of the circular truncated cone, and combining the circular truncated cone with the generated circular truncated cone if the non-textured area exists; or else, the surface texture of the circular truncated cone is unfolded to generate a plane texture unfolding picture, and the texture on the surface of the porcelain is unfolded to the novel technology on the two-dimensional plane from the surface of the three-dimensional object based on a surface parameterization method.
Description
Technical Field
The invention belongs to the field of computer graphics, and particularly relates to an automatic generation method of a texture expansion diagram for rotationally symmetric porcelain.
Background
And (3) parameterizing the mesh surface, namely establishing a mapping relation so that the vertex on the mesh surface is mapped into the parameter area through the mapping relation. Parameterization methods can be divided into two main categories, depending on the parameterization target: (1) directly using coordinate transformation; (2) parameterization is achieved using an auxiliary surface or geometry as an intermediary. Mapping an inextensible three-dimensional mesh surface to a plane will inevitably produce distortion in length, area, and angle. Many approaches focus on reducing the distortion caused by parameterization while preserving geometric metrics, such as constructing a linear approximation to a non-linear harmonic map by minimizing the Dirichlet energy of the map; the effect of linear mixing on the final distortion of both the area and angle of coverage is balanced by a parameter, and then the distortion energy function of the linear mixing is minimized. In our method, we use the circular table as an intermediary for parameterization.
Fitting the circular truncated cone: the point cloud data is geometrically fitted by surrounding all points in the point cloud data with a simple geometric shape and minimizing the volume of the geometric shape. Many researchers have made great progress in fitting point cloud data using a cylinder. However, in practice, all problems cannot be solved well by simply fitting a three-dimensional object by using a cylinder, and for a device to be processed, fitting by using a cone is a more effective method. The quasi-least squares method is a common method for fitting quadratic surfaces such as cylindrical surfaces and conical surfaces.
Disclosure of Invention
The invention provides an automatic generation method of a rotary symmetry porcelain-oriented texture expansion diagram, and aims to solve the problems in the prior art.
In order to solve the problems in the prior art, the invention provides the technical scheme that:
1. an automatic generation method of a pattern development diagram facing a rotational symmetry porcelain comprises the following steps:
inputting data information of a model with two-dimensional textures;
secondly, obtaining an upright model based on the symmetry axis rotation model, and further obtaining front views of the upright model in front, back, left and right directions;
analyzing the four obtained front views by using a gradient operator to generate a cumulative gradient map of the model;
step four, calculating a model cutting plane on the basis of the obtained cumulative gradient map to complete the segmented processing of the model;
step five, performing circular truncated cone fitting on each obtained segmented model;
step six, judging whether a non-textured special area exists in the fitting of the circular truncated cone, and combining the circular truncated cone with the generated circular truncated cone if the non-textured area exists; otherwise, the surface texture of the circular truncated cone is unfolded to generate a plane texture unfolded drawing.
And in the third step, the gradient diagram is a front view obtained in four directions of the front, the back, the left and the right of the model in an orthographic projection mode, the vertical gradient distribution of the four front views is respectively calculated by utilizing a gradient operator, and the sum of absolute values of the front views is accumulated along the horizontal direction to obtain the distribution of the sum of absolute values of the gradient of one dimension.
The cutting line plane is a position where the sum of absolute values of the gradients is changed violently, and the position of the cutting line is searched by using a formula (1):
wherein L isiWhich represents the (i) th row of the picture,
the gradient of the ith row is expressed as an artificially set threshold value, LCIndicating the cut line found. In the step five, the circular table fitting can obtain an expansion plane through the following formula (2):
wherein the content of the first and second substances,
wherein (X, Y, z) represents a point in a three-dimensional space, (X, Y) represents a point on a two-dimensional plane corresponding thereto, hAnd R represents the height and radius of the circular table passing through the point (x, y, z) and being parallel to the bottom surface of the original circular table, respectively, H and R represent the height and radius of the original circular table, respectively, yAThe y coordinate value of A is shown, and theta represents the central angle of the sector after the circular truncated cone is unfolded.
Eliminating the overlapping area in the unfolding plane by the following formula (3);
wherein the content of the first and second substances,
and
representing the upper and lower boundaries of segment i, respectively.
The step six, merging the non-texture region and the generated circular truncated cone, comprises the following steps:
first, determining whether the gradient value of a non-texture region is less than a given threshold value;
second, the non-textured region is merged with its neighboring regions having a radius close to its radius by equation (4)
Wherein, CiDenotes the ith round table, RiThe radius of the lower bottom surface of the ith circular truncated cone is shown;
thirdly, fitting the circular truncated cone and unfolding the plane again according to the combined result.
Advantageous effects
The method is based on the acquisition of a model cutting plane, and the model is divided into segments which can be approximately fitted by a circular table through the cutting plane, so that the approximate unfolding of the porcelain surface texture with rotational symmetry from a three-dimensional model to a two-dimensional plane is realized by a circular table unfolding formula. The invention has the following advantages:
(1) the texture segmentation can be automatically realized. Compared with the existing texture segmentation method, the method can achieve the expected effect of texture segmentation.
(2) The method relates to the adjustment of the layout after the layout is unfolded to the plane, and achieves the purpose of convenient observation.
(3) Compared with the traditional archaeological drawing, the invention not only reduces the time required by drawing, saves manpower and material resources, but also reduces the requirement of touching precious objects with bodies, thereby achieving the purpose of protecting the objects.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a position image of the present invention for finding texture segmentation on porcelain by gradient operator; wherein: (a) the front view of the model in four directions, namely front, back, left and right directions is shown, the graph (b) is a gradient graph drawn by matlab, and the graph (c) is a found cutting plane;
FIG. 3 is an expanded view of the truncated cone of the present invention;
FIG. 4 is a view of a particular situation encountered with the unwinding of a circular table in the present invention; in the figure, (a) represents a model and a cutting plane, and (b) represents a horizontal cutting plane passing through one vertex and one edge of a triangular patch; FIG. (c) shows a horizontal cutting plane passing through both edges of a triangular patch; FIG. (d) shows a vertical cutting plane through the triangular patch, resulting in the unfolded triangular patch being distributed over the boundaries of the unfolding plane;
FIG. 5 is an adjustment of the expanded two-dimensional layout of the present invention: FIG. (a) is a diagram showing the result before layout adjustment; fig. (b) is a diagram showing the result of the layout adjustment.
FIG. 6 is a merged view of the non-textured areas of the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a method for automatically generating a pattern development view for a rotationally symmetric porcelain, comprising the steps of:
step one 101, inputting model data information with two-dimensional texture;
step two 102, rotating the upright model based on the symmetry axis direction to further obtain front views of the upright model in the front, back, left and right directions; step three 103, analyzing the four obtained front views by using a gradient operator to generate an accumulated gradient map of the model;
the analysis based on the gradient operator specifically comprises the steps of calculating vertical gradients of the front view of the model in four directions by utilizing a Sobel gradient operator, and accumulating the sum of absolute values of the front view along the horizontal direction to obtain the distribution of the sum of the absolute values of the one-dimensional gradients.
Step four 104, calculating a model cutting plane on the basis of the obtained cumulative gradient map to complete the segmentation processing of the model;
a) the position of the cutting line is defined as the position where the sum of the absolute values of the gradients changes sharply, and the position of the cutting line is found by using the formula (1):
wherein L isiWhich represents the (i) th row of the picture,
the gradient of the ith row is expressed as an artificially set threshold value, LCRepresenting the found cut line.
b) The cut lines found on the image are mapped onto the three-dimensional model according to the principle of orthographic projection, so as to obtain the position of the cut plane.
Step five 105, performing circular truncated cone fitting on each obtained segmented model;
the fitting and development formula derivation based on the deployable curved surface circular truncated cone comprises the following steps:
a) and segmenting the model according to the cutting plane, and performing approximate fitting of a circular truncated cone on the obtained segmented model segment.
b) And unfolding the fitted circular truncated cone according to a plane unfolding formula deduced by us.
c) When the triangular patch is penetrated by the cutting plane or the unfolding plane, the triangular patch needs to be split into sub-triangular patches along the cutting plane or the unfolding plane and then unfolded respectively.
Wherein the adjustment of the layout after the expansion to the plane comprises the following steps:
a) the bounding box size of each texture segment after unfolding is calculated.
b) Moving the vertical positions of the other segments, with reference to the lowest texture segment, so that the bounding boxes of the segments are tangent, the vertical position calculation is defined by equation (2):
wherein the content of the first and second substances,
and
representing the upper and lower boundaries of segment i, respectively.
Step six 106, judging whether a non-textured special area exists in the fitting of the circular truncated cone, if so, merging the non-textured special area with the generated circular truncated cone, and returning to the step five 105; the method for combining the non-texture areas comprises the following steps:
a) the positions of the non-textured regions are determined and the ones with similar radii in adjacent round tables are selected for merging 107.
b) And fitting and unfolding the circular truncated cone again according to the combined result. Otherwise, the surface texture expansion of the circular truncated cone is carried out to generate planes (108,109) with two-dimensional textures.
As shown in fig. 2, for a three-dimensional porcelain model having rotational symmetry, first, the symmetry axis is calculated by a commonly used symmetry axis estimation method, and the model is rotated until the orientation of the symmetry axis coincides with the vertical direction of the coordinate system. Wherein (a) is a front view of the model in the front, back, left and right directions, the front views of the model in the front, back, left and right directions are obtained through an orthographic projection mode, the vertical gradient distribution of the four front views is respectively calculated by utilizing a Sobel gradient operator, the sum of absolute values of the front views is accumulated along the horizontal direction, and the distribution of the one-dimensional gradient absolute value sum is obtained, namely, the graph (b) is a gradient graph drawn by matlab. Then, the position where the sum of the absolute values changes most is determined by equation (1), and this position is taken as the position of the cutting line.
Wherein L isiWhich represents the (i) th row of the picture,
the gradient of the ith row is expressed as an artificially set threshold value, LCIndicating the cut line found.
Wherein, the graph (c) shows that the ratio of the distance from the top point of the model to the cutting plane to the height of the model satisfies the equal proportion relation in the two-dimensional front view and the three-dimensional space according to the principle of orthographic projection. We can map the obtained cut line to three-dimensional space to obtain the location of the model cut plane.
As shown in fig. 3, the model is divided according to a cutting plane, and the triangular patch of the model is divided into different model segments. And for the model segment obtained after the segmentation, projecting all vertexes of the triangular patch contained in the segment to an orthographic view vertical to a horizontal plane through orthographic projection, and fitting a circular truncated cone contour line with a minimum area by using the projected vertexes. Based on the fitted round table, we can deduce the expansion formula from the round table to the plane:
wherein the content of the first and second substances,
wherein (X, Y, z) represents a point in a three-dimensional space, (X, Y) represents a point on a two-dimensional plane corresponding thereto, H and R represent the height and radius of a circular table passing through the point (X, Y, z) and being parallel to the bottom surface of the original circular table, respectively, H and R represent the height and radius of the original circular table, respectively, YAY coordinate value representing A, theta represents the development of the circular truncated coneThe central angle of the rear sector. The specific meaning of each symbol is shown in figure 3.
As shown in fig. 4, it is noted that several special cases are encountered during the unfolding process, requiring separate processing:
i. the triangular patch is divided into upper and lower parts by a horizontal cutting plane, see fig. 3. The triangle traversed by the cutting plane now needs to be divided into two parts. For each part, directly expanding if the part is a triangle; if the square is formed, the diagonal line of the square is connected, and the square is divided into two triangles to be unfolded respectively.
The triangular patch is divided into left and right parts by the initial unfolding plane, in which case the unfolding results, if done directly, are shown in fig. 3. So we also need to divide into two parts to be deployed separately.
As shown in fig. 5, for the adjustment of the layout after unfolding to the plane: each segmented model segment is subjected to circular truncated cone fitting and planar expansion and then falls on a plane, and mutual overlapping can be generated. The step is used for adjusting the vertical position of the unfolded segment on the plane, eliminating mutual overlapping and forming a two-dimensional ornamentation unfolded image convenient to observe. One possible approach is to calculate the bounding box of each expanded texture segment and adjust the positions of the other segments according to equation (3) with respect to the lowest segment so that the bounding boxes of adjacent segments are tangent;
wherein the content of the first and second substances,
and
representing the upper and lower boundaries of segment i, respectively.
As shown in fig. 6, the non-texture region merging includes the following steps:
the surface texture of the three-dimensional model may present partially substantially empty regions, which are mostly narrow segments. This step combines such segments with adjacent segmented segments to produce a more coherent texture unfolding result. One possibility is to first determine the region with gradient value smaller than the given threshold value as a non-textured region, then merge it with the neighboring region close to its radius (defined by equation 4), and re-perform the fitting of the circular truncated cone and the plane unfolding according to the merged result.
Wherein, CiDenotes the ith round table, RiThe radius of the lower bottom surface of the ith circular truncated cone is shown;
the input of the algorithm is a three-dimensional model pasted with textures, the front views of the front, the rear, the left and the right of the model are obtained by rotating an object through obtaining a symmetry axis of the model, the vertical gradient distribution of the four front views is respectively calculated by utilizing a sobel gradient operator, and the sum of absolute values of the gradients of the front views is obtained along the horizontal direction. And searching a cutting plane of the model on the obtained gradient map, thereby realizing the segmentation of the model. And then performing circular truncated cone fitting on each segmented model. For a special region without texture generated by segmentation, the similarity of the radius of the region and the radius of the upper and lower adjacent regions is compared to realize the combination of the regions without texture. And realizing the segmentation expansion of the surface texture of the segmentation model by using an expansion formula. And moving the textures by solving the surrounding box of each section of the textures for the two-dimensional textures unfolded to the plane, so that the textures are not overlapped with each other, and the aim of optimizing the unfolding result is fulfilled.
Claims (6)
1. An automatic generation method of a pattern development diagram facing a rotational symmetry porcelain is characterized by comprising the following steps:
inputting model data information with two-dimensional textures;
secondly, obtaining an upright model based on the symmetry axis rotation model, and further obtaining front views of the upright model in front, back, left and right directions;
analyzing the four obtained front views by utilizing a gradient operator to generate an accumulated gradient map of the model;
step four, calculating a model cutting plane on the basis of the obtained cumulative gradient map to complete the segmented processing of the model;
step five, performing circular truncated cone fitting on each obtained segmented model;
step six, judging whether a non-textured special area exists in the fitting of the circular truncated cone, if so, merging the non-textured area with the generated circular truncated cone, and returning to the step five; otherwise, the surface texture of the circular truncated cone is unfolded to generate a plane texture unfolded drawing.
2. The method as claimed in claim 1, wherein the gradient map in the third step is a front view obtained by orthographic projection in four directions, namely front, back, left and right directions of the model, wherein the vertical gradient distribution of the four front views is calculated by a gradient operator, and the one-dimensional distribution of the sum of absolute gradient values is obtained by accumulating the sum of absolute values of the front views in the horizontal direction.
3. The method of automatically generating a pattern development view for a rotationally symmetric porcelain according to claim 2, wherein the cutting plane is a position where the sum of absolute values of gradients changes drastically, and the position of the cutting line is found by using formula (1):
wherein L isiWhich represents the (i) th row of the picture,
the gradient of the ith row is expressed as an artificially set threshold value, LCIndicating the cut line found.
4. The method for automatically generating the texture development map for the rotationally symmetric porcelain according to claim 1, wherein the circular table fitting in the fifth step can obtain the development plane through the following formula (2):
wherein the content of the first and second substances,
wherein (X, Y, z) represents a point in a three-dimensional space, (X, Y) represents a point on a two-dimensional plane corresponding thereto, H and R represent the height and radius of a circular truncated cone passing through the point (X, Y, z) and parallel to the bottom surface of the cone, respectively, H and R represent the height and radius of the cone, respectively, YAThe y coordinate value of A is shown, and A shows the extending intersection point of the generatrix of the circular truncated cone; θ represents the central angle of the fan after the circular truncated cone is unfolded.
5. The automatic generation method of the texture development map for the rotationally symmetric porcelain according to claim 4, characterized in that the elimination of the overlapped area in the development plane is performed by the following formula (3);
wherein the content of the first and second substances,
and
representing the upper and lower boundaries of segment i, respectively.
6. The method for automatically generating the texture development map for the rotationally symmetric porcelain according to claim 1, wherein the step six of combining the non-textured area with the generation circular truncated cone comprises the steps of:
firstly, determining a region with a gradient value smaller than a given threshold value as a non-texture region;
second, the non-textured region is merged with its neighboring regions having a radius close to its radius by equation (4)
Wherein, CiDenotes the ith round table, RiThe radius of the lower bottom surface of the ith circular truncated cone is shown;
thirdly, fitting the circular truncated cone and unfolding the plane again according to the combined result.
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