A method for triangulation of plant cells

Abstract

This invention discloses a method for triangulation of plant cells. The method includes: sampling slice points and recording points calculated from the inner and outer sides of the cell wall and equidistant lines on each plane; using the midpoints of the first and last equidistant lines and the calculated points on the inner and outer sides of the cell wall as dividing lines; then sorting the points on the bottom surface from top to bottom according to the perpendicular points of the dividing lines to the inner and outer sides; performing scan-line triangulation using the sorted inner and outer sides and the dividing lines; calculating the number of lines connecting the inner and outer sides of the plane with fewer points based on nip and nil values; and using the number of lines to record triangles according to certain rules to complete lateral triangulation. This invention can achieve plant cell triangulation using a relatively simple method, which can be easily applied to practical needs; this method has low triangulation time, with both time and space complexity being linear, which is beneficial for subsequent research on plant cell properties.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional visualization technology, and in particular to a method for triangulation of plant cells. Background Technology

[0002] Plant cell visualization technology plays a crucial role in studying plant cell properties and simulating plant cell growth. Among various techniques for achieving 3D visualization, 3D triangulation is an indispensable key step. Currently, commonly used algorithms such as Delaunay are general-purpose triangulation algorithms. However, with the increasing sampling resolution of plant cells, using general-purpose algorithms like Delaunay may lead to the neglect of many sampling points during triangulation. Currently, there are few effective and available 3D triangulation methods for plant cells. Therefore, research on 3D triangulation algorithms for plant cells has significant theoretical and practical value. Summary of the Invention

[0003] Traditional triangulation methods struggle to accurately reconstruct the elongated cellular structures in plants, affecting the precision of the reconstructed plant cells. To overcome the limitations of existing algorithms in practical applications, this invention aims to provide a novel method for three-dimensional triangulation of plant cells, which can be implemented in a relatively simple manner, as detailed below:

[0004] A method for triangulation of plant cells, the method comprising:

[0005] Slice points are sampled, and the points calculated from the inner and outer sides of the cell wall and the equidistant lines of each plane are recorded.

[0006] Use the midpoint between the first and last equally spaced lines and the midpoint of the points calculated on the inner and outer sides of the cell wall as dividing lines. Then, sort the points on the bottom surface from top to bottom according to the perpendicular points of the dividing lines to the inner and outer sides. Use the sorted inner and outer sides and the dividing lines to perform the scan line triangulation method.

[0007] The number of lines connecting the inner and outer points of a plane with fewer points is calculated based on the nip and nil values. The number of lines is then used to record triangles according to certain rules to complete the lateral triangulation.

[0008] Specifically, the sampling of slice points, which records the points calculated from the inner and outer sides of the cell wall and the equidistant lines of each plane, is as follows:

[0009] First, the plant cell is divided into several planes parallel to the XOY plane along the Z-axis at equal intervals. Then, N equally spaced lines parallel to the coordinate axes and in the same position on each plane are drawn in each plane. Then, the three-dimensional coordinate values, plane number and point number of the generated cell wall outer and inner points are recorded separately.

[0010] The closed plane geometry formed by connecting all the outer points or all the inner points in the first or last plane is the base. The part of the closed curved surface of the cell wall corresponding to all the outer points of the cell wall in all planes or all the inner points of the cell wall in all planes, excluding the base, is the side surface.

[0011] Furthermore, the specific method of triangulating the base of plant cells is as follows:

[0012] Draw a dividing line by connecting the first and last equidistant lines to the midpoint of the points calculated on the outer side of the cell wall; draw a perpendicular line to each inner and outer point on the dividing line, and then sort the points from top to bottom according to their positions on the perpendicular line, and scan the sorted inner and outer points.

[0013] If the current scan point is on the same side as the top element of the stack, and the slope of the vector formed by the scan point and the vertex and the secondary vertex in the stack is less than the slope of the split line, or if the scan point is below the split line and the slope of the vector formed by the scan point and the vertex and the secondary vertex in the stack is greater than the slope of the split line, then record the triangle formed by the scan point and the vertex and the secondary vertex in the stack; otherwise, push the scan point onto the stack.

[0014] If the current scan point is on the opposite side of the top element of the stack, pop the elements in the stack in sequence to form a triangle with the scan point.

[0015] Furthermore, the scanning points change from top to bottom in order of the perpendicular points on the perpendicular line. Taking the dividing line as the boundary, if the coordinates of the current scanning point are above the dividing line and the slope of the vector V is greater than or equal to the slope of the dividing line, or if the coordinates of the scanning point are below the dividing line and the slope of the vector V is less than or equal to the slope of the dividing line, the current scanning point C is pushed onto the stack; otherwise, the vertex T in the stack is popped from the stack and the triangle STC is recorded.

[0016] Wherein, the nip value is the remainder of n2 and n1, and the size of the nip value represents how many insertion points are in the plane with fewer inner and outer points; the nil value represents the minimum number of line segments that each point in the plane with fewer points needs to be connected; the value of nil is the quotient of n2 and n1 rounded down and then 1, where n1 is the number of inner and outer points in the plane with fewer inner and outer points, and n2 is the number of inner and outer points in the plane with more inner and outer points.

[0017] Furthermore, each point on the plane with fewer points is initially assigned the value nil. Then, the insertion point is calculated nip times in a loop. The insertion point is calculated as: round((n1*i) / (nip+1)), where the round function represents rounding the result.

[0018] The recording triangle STC is as follows: for the plane with fewer points, the current inner and outer points are set as P1; for the plane with more points, the current inner and outer points are set as P2; and for the plane with more points, the next inner and outer points are set as P3. The inner and outer points in the plane are connected end to end to form a loop.

[0019] Based on the index of P1 and the connection count array r, obtain the connection count L of P1. Repeat L-1 times. In each cycle, P1 remains unchanged, and P2 and P3 are the next inner and outer points of the original inner and outer points respectively. Record triangle P1P2P3.

[0020] When the loop reaches the (L-1)th iteration, after recording triangle P1P2P3, it is also necessary to record triangle P1P3P4, where P4 is the next inner or outer point of the plane containing P1.

[0021] The beneficial effects of the technical solution provided by this invention are:

[0022] 1) This invention can achieve triangulation of plant cells using a relatively simple method, and can be easily applied to practical needs;

[0023] 2) This method has a short partitioning time and linear time and space complexity, which is beneficial for subsequent research on plant cell properties. Attached Figure Description

[0024] Figure 1 A flowchart of a plant cell triangulation method;

[0025] Figure 2 A schematic diagram of plant cell sampling results;

[0026] Figure 3 This is a schematic diagram showing the sorting of inner and outer points along the dividing line;

[0027] Figure 4 This is a diagram illustrating the first step of triangulation of the base surface.

[0028] Figure 5 This is the second step diagram for the triangulation of the base surface;

[0029] Figure 6 This is the third step diagram for the triangulation of the base surface;

[0030] Figure 7 This is the fourth step diagram for the triangulation of the base surface;

[0031] Figure 8 This is the fifth step diagram for the triangulation of the base surface;

[0032] Figure 9 This is a schematic diagram of the side triangulation.

[0033] Figure 10This is a diagram showing the effect of triangulation on the side.

[0034] Figure 11 A diagram showing the triangulation effect of plant cells. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0036] Example 1

[0037] This invention provides a method for triangulation of plant cells, such as... Figure 1 As shown, it includes the following steps:

[0038] Step 101: To better triangulate plant cells, point sampling is required. Sampling points are calculated from the cell wall and equidistant lines of each plane within the plant cell. See the sampling results below. Figure 2 .

[0039] Step 102: Perform bottom triangulation on the plant cells. Use the midpoint between the first and last equally spaced lines and the midpoint of the points calculated on the inner and outer sides of the cell wall as the dividing line. Then sort the inner and outer points on the bottom surface from top to bottom according to the perpendicular points of the dividing line. Use the sorted inner and outer points and the dividing line to perform scan line triangulation.

[0040] Among them, see Figure 3 Line L1 is the dividing line, line L2 is the first equally spaced line, and line L3 is the last equally spaced line. It includes 1-10 inner and outer points, with the midpoints being p1 and p2. The 1-10 inner and outer points are sorted.

[0041] Step 103: Perform lateral triangulation on the plant cells. Lateral triangulation requires calculating the nip and nil values. Then, based on the nip and nil values, calculate the number of lines connecting the inner and outer points of the plane with fewer points. Use the number of lines to record triangles according to certain rules to complete the lateral triangulation.

[0042] Step 101 includes:

[0043] The sampling points generated on each plane are numbered in ascending order of size, starting from 1. The three-dimensional coordinates of the sampling points, as well as the plane number and point number, are recorded.

[0044] Step 102 includes:

[0045] 1) Connect the first and last equidistant lines and the midpoint of the points calculated on the outer side of the cell wall to form a dividing line; draw a perpendicular line from each inner and outer point to the dividing line, and then sort the points from top to bottom according to their positions on the perpendicular line, and scan the sorted inner and outer points.

[0046] 2) If the current scan point is on the same side as the top element of the stack, and the slope of the vector formed by the scan point and the vertex and the second vertex in the stack is less than the slope of the split line, or the scan point is below the split line and the slope of the vector formed by the scan point and the vertex and the second vertex in the stack is greater than the slope of the split line, then record the triangle formed by the scan point and the vertex and the second vertex in the stack; otherwise, push the scan point onto the stack.

[0047] 3) If the current scan point is on the opposite side of the top element of the stack, pop the elements in the stack in turn to form a triangle with the scan point.

[0048] In summary, the embodiments of the present invention achieve triangulation of plant cells through the above steps 101-103, which is time-saving, simple, and can be easily applied to practical needs.

[0049] Example 2

[0050] The following is combined Figure 1 The solution in Example 1 will be further described below:

[0051] 201: Sampling of plant cell sections;

[0052] First, the plant cell is divided into several planes parallel to the XOY plane along the Z-axis at equal intervals. Then, N equally spaced lines parallel to the coordinate axes and coinciding on each plane are drawn within each plane. Next, the three-dimensional coordinates, plane numbers, and point numbers of the generated outer and inner cell wall points are recorded separately. The closed plane geometry formed by connecting all outer or inner points in the first or last plane is the base. The portion of the closed surface of the cell wall corresponding to all outer or inner cell wall points in all planes, excluding the base, is the lateral surface. See the final sampling results below. Figure 2 .

[0053] 202: Triangular division of the base;

[0054] In this embodiment of the invention, the triangulation algorithms for the bottom and side faces are independent of each other. If it is the bottom face, the triangulation algorithm for the bottom face is performed, and the detailed steps are as follows:

[0055] 1) Draw dividing lines on the bottom surface

[0056] To divide the base into two parts for triangulation, a dividing line needs to be drawn on the base. (See also...) Figure 3 Calculate the midpoints of the first equidistant line L2 and the last equidistant line L3 with the points calculated on the outer side of the cell wall (p1 is the midpoint of the first equidistant line L2 with the points calculated on the outer side of the cell wall, and p2 is the midpoint of the last equidistant line L3 with the points calculated on the outer side of the cell wall). Set the coordinates of these two midpoints as x1, y1, x2, y2. The dividing line passes through these two midpoints, therefore the slope of the dividing line is k = (y2 - y1) / (x2 - x1), and the intercept is b = y1 - k * x1. The segmentation effect is as follows: Figure 3 As shown, the straight line L1 is the dividing line.

[0057] 2) Sort the inner and outer points

[0058] Scan line triangulation requires sorting the inner and outer points along the dividing line from top to bottom. Since the dividing line is not necessarily perpendicular to the X or Y axis, each inner and outer point needs to be perpendicular to the dividing line. The points are then sorted from top to bottom based on their positions on the dividing line to determine the scanning order of the inner and outer points in scan line triangulation. (See also...) Figure 3 The 1-10 inner and outer points are sorted inner and outer points.

[0059] 3) Scanline triangulation method

[0060] The scan line is perpendicular to the dividing line. The inner and outer points processed each time are those touched by the current scan line. A linear list with restricted operations, called a stack, is used here, where elements can only be inserted and deleted at the end of the list. During the algorithm's execution, the scan points always change from top to bottom in the order of the perpendicular points on the dividing line. Then, using the dividing line as a boundary, if the coordinates of the current scan point are above the dividing line, F=1 is marked; otherwise, if the coordinates of the current scan point are below the dividing line, F=0 is marked.

[0061] 4) The current scan point is on the same side as the point stored at the top of the stack.

[0062] If the current scan point is on the same side as the point stored at the top of the stack, it is necessary to determine whether to pop the triangle and record it based on the direction of the vector V formed by the current scan point C, vertex T in the stack, and the second-highest vertex S in the stack, and the position of the dividing line, where V = S - T + CT. If the coordinates of the scan point are above the dividing line and the slope of V is greater than or equal to the slope of the dividing line, or if the coordinates of the scan point are below the dividing line and the slope of V is less than or equal to the slope of the dividing line, then push the current scan point C onto the stack. Otherwise, pop vertex T from the stack and record triangle STC. Repeat step 4) to continue determining whether the current scan point C, vertex T, and second-highest vertex S in the stack can be popped and a triangle recorded. When only one inner / outer point remains in the stack, push the current scan point C onto the stack.

[0063] 5) The current scan point is on the opposite side of the point stored in the stack.

[0064] The scan point C is on the opposite side of all points in the stack. At this point, point C can form a triangle with any point in the stack through an interior diagonal. Therefore, we continuously cut the triangle formed by C and the vertices and sub-vertices of the stack, while popping the top point from the stack. This process continues until only one element remains in the stack. Then, the bottom element is popped from the stack, the first previously encountered top element T is pushed onto the stack, and finally, the scan point C is pushed onto the stack.

[0065] 203: Lateral triangulation

[0066] Lateral triangulation requires the inner and outer points of the current plane and the inner and outer points of the plane in the previous layer. The number of inner and outer points in the two layers is compared. Let n1 be the number of inner and outer points of the plane with fewer inner and outer points, and n2 be the number of inner and outer points of the plane with more inner and outer points. The steps of lateral triangulation are as follows:

[0067] 1) Calculate nip and nil values

[0068] The nip value is the remainder of n2 and n1. The size of the nip value represents how many insertion points are needed on the plane with fewer points on the inner and outer sides. The nil value represents the minimum number of line segments that each point on the plane with fewer points needs to be connected to. The value of nil is the quotient of n2 and n1 rounded down and then incremented by 1.

[0069] 2) Calculate the number of lines connecting the inner and outer points.

[0070] After calculating the nip and nil values, we can use these two values ​​to generate the number of connections for each point on the plane with fewer points. First, we initialize each point on the plane with fewer points to nil. Then, we iterate nip times to calculate the connection points. The calculation method for the connection points is: round((n1*i) / (nip+1)), where n1 is the number of inner and outer points on the plane with fewer inner and outer points, i is the iteration variable in the loop, nip is the remainder between n2 and n1, and the round function represents rounding the result. Finally, the number of connections for each inner and outer point is calculated and stored in the r array.

[0071] 3) Record the triangle

[0072] After obtaining the number of lines connecting the inner and outer points, we can connect the two planes to record the triangle based on the number of lines connecting each inner and outer point. For the plane with fewer points, we iterate through its inner and outer points, see [link to documentation]. Figure 9Let P1 be the currently traversed inner and outer points, P2 be the current inner and outer points of the plane with more points, and P3 be the next inner and outer points of the plane with more points. Connect the inner and outer points in the plane to form a loop. Obtain the number of connections L for P1 based on the index of P1 and the connection count array r. Repeat this L-1 times, keeping P1 unchanged in each iteration, and setting P2 and P3 as the next inner and outer points of the original inner and outer points, recording triangles P1P2P3. When the loop reaches the L-1st iteration, after recording triangles P1P2P3, it is also necessary to record triangle P1P3P4, where P4 is the next inner and outer point of the plane containing P1.

[0073] Example 3

[0074] Taking bamboo cells as an example, the three-dimensional coordinates of the sampling points, as well as the plane number and point number data, are saved as a .mat file.

[0075] Draw a dividing line on the bottom surface, and sort the sampling points from top to bottom according to the perpendicular points on the dividing line. Figure 3 The inner and outer points are sorted, with line L1 as the dividing line; then the scan line triangulation method is performed, and the stack is emptied before that.

[0076] Scan point 1: Since the current stack element is empty, the inner and outer points of point 1 are directly pushed onto the stack.

[0077] Scan point 2: Scan point 2 is on the opposite side of the inner and outer sides of the top of the stack, point 1. Since there are fewer than 2 elements in the stack, the inner and outer sides of point 2 are directly pushed onto the stack.

[0078] Scan point 3: Scan point 3 is on opposite sides of the inner and outer sides of the top of the stack, which is point 2. Since there are two elements in the stack at this time, they can form a triangle. Therefore, record triangle 123, pop inner and outer sides 1 and 2 from the stack, and push inner and outer sides 2 and 3 back onto the stack, as follows. Figure 4 As shown.

[0079] The scan point is number 4: Scan point 4 is on the same side as the inner and outer points of the stack top 3. The scan point, the stack vertex and the second vertex form a vector V = (-0.2, -12.5). At the same time, the scan point is above the dividing line and the slope of vector V is greater than the slope of the dividing line. Therefore, the inner and outer points of number 4 are pushed onto the stack.

[0080] Scan point 5: Scan point 5 is on the opposite side of the inner and outer sides of the top of the stack, point 4. Record triangles 543 and 532. Pop the inner and outer sides of points 4, 3, and 2 from the stack, and push the inner and outer sides of points 4 and 5 back onto the stack. Figure 5 and Figure 6 As shown.

[0081] Scan point 6: Scan point 6 is on the same side as the inner and outer points of the stack top 5. The plotted point, along with the stack vertex and secondary vertex, forms vector V = (0.2, 2.5). Simultaneously, the scan point is below the dividing line, and the slope of vector V is greater than the slope of the dividing line. Record triangle 654. Pop the inner and outer points of 5 from the stack and push the inner and outer points of 6 onto the stack, as shown below. Figure 7 As shown.

[0082] The operation for the remaining scan points is as described above. Figure 8 This is a rendering of the effect of triangulation of the bottom surface.

[0083] Figure 10 It is a side triangulation diagram formed by the bottom surface and the plane of the second slice of the plant. Since the number of points on the inner and outer sides of the two planes is the same, which is 8, the nip value is 0, which means there are no interpolation points; the nil value is 2, that is, the value of the r array is 2. Each point on the bottom surface has two connecting lines.

[0084] Start recording the triangle from the inner and outer points of the base, starting with point 1.

[0085] Point 1 (inner and outer): r(1) = 2, repeat 2 times. Point 1 (inner and outer) has two connecting lines 1-9 and 1-10. The first cycle records triangle 1 9 10, and the last cycle records triangle 1 10 2. Here, point 2 (inner and outer) is the next inner and outer point of point 1 (inner and outer) on the bottom surface.

[0086] Point 2, inner and outer: r(1) = 2, cycle 2 times, there are two connecting lines 2-10 and 2-11 for point 2, the first cycle records triangle 2 10 11, the last cycle records triangle 2 11 3, here point 3, inner and outer is the next inner and outer point of point 2 on the bottom.

[0087] The operation of the remaining inner and outer points is as above. It is particularly important to note that when the loop reaches the last inner and outer point, point 8, the line connecting point 8 is 8-16 and 8-9 instead of 8-17, and the recorded triangles are 8 16 9 and 8 9 1.

[0088] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for triangulation of plant cells, characterized in that, The method comprises: Slicing point sampling, recording the points calculated by the inside and outside of the cell wall and the equidistant lines of each layer plane; Taking the midpoint of the points calculated by the inside and outside of the cell wall as the dividing line of the first and last equidistant lines, and then sorting the vertical points of the inside and outside points on the bottom surface from top to bottom, and using the sorted inside and outside points and the dividing line to perform the scan line triangulation method; The side triangulation needs the inner and outer points of the current plane and the inner and outer points of the last plane, compares the number of the inner and outer points of the two layers, and calculates the number of the connecting lines of the inner and outer points of the plane with less points according to the value and the value The value and the value calculates the number of the connecting lines of the inner and outer points of the plane with less points, and records the triangles according to certain rules to complete the side triangulation; The value represents how many inserting points the plane with less points has; The value represents the number of the connecting lines of each point of the plane with less points; The scan line triangulation method is: Connecting the midpoint of the points calculated by the outside of the cell wall and the first and last equidistant lines as the dividing line; each inside and outside point is perpendicular to the dividing line, and the vertical points are sorted in top-to-bottom order according to their positions on the vertical line; the scanned points are scanned according to the sorted inside and outside points; if the current scanning point is on the same side as the top element of the stack, when the scanning point is above the dividing line and the slope of the vector formed by the scanning point and the top and second top points in the stack is less than the slope of the dividing line, or when the scanning point is below the dividing line and the slope of the vector formed by the scanning point and the top and second top points in the stack is greater than the slope of the dividing line, then the triangle formed by the scanning point and the top and second top points in the stack is recorded, otherwise the scanning point is stacked; The triangle is recorded according to a certain rule: The inner and outer points are connected by lines. Based on the number of lines connecting each inner and outer point, two planes are connected to record the triangle. For the plane with fewer points, its inner and outer points are traversed. Let the currently traversed inner and outer points be... The plane with more points currently has inner and outer points. For a plane with more points, the next inner and outermost point of the current inner and outermost point is... The points on the inner and outer sides of the plane, when connected end to end, form a ring. According to... subscript and connection number array To obtain Number of lines ,cycle Each cycle constant, , Record the next inner and outer points of the triangle, which are the original inner and outer points respectively. When the loop reaches the th At this time, after recording the triangle The triangle also needs to be recorded later. , yes The next inner or outer point of the plane.

2. The method of claim 1, wherein, The slicing point sampling, recording the points calculated by the inside and outside of the cell wall and the equidistant lines of each layer plane is specifically: First, the plant cell is divided into several planes along the Z-axis equidistant parallel XOY plane, secondly, N equidistant lines parallel to the coordinate axes and located at the same position on each plane are drawn, and then the three-dimensional coordinate values and plane number and point number of the generated cell wall outside points and inside points are recorded separately; Wherein the closed plane geometry formed by connecting all the outside points or all the inside points in the first or last plane is the bottom surface, and the part removed from the closed surface of the cell wall corresponding to all the cell wall outside points of all planes or all the cell wall inside points of all planes is the side surface.

3. The method of claim 1, wherein the plant cell is a leaf cell. If the current scanning point is on the opposite side of the top element of the stack, the elements in the stack are popped out in turn to form the triangulation triangle with the scanning point.

4. The method of claim 1, wherein, The scanning point changes from top to bottom according to the order of the vertical point on the vertical line, and the current scanning point is stacked if the coordinate of the scanning point is above the segmentation line and the slope of the vector is greater than or equal to the slope of the segmentation line or if the coordinate of the scanning point is below the segmentation line and the slope of the vector is less than or equal to the slope of the segmentation line. ​​​ Otherwise, pop the top vertex from the stack and record the triangle .

5. The method of claim 1, wherein the plant cell is a leaf cell. The value is the remainder of the quotient of the value of the quotient of the quotient of the number of inner and outer points of the plane with fewer inner and outer points, the number of inner and outer points of the plane with more inner and outer points.

6. A method of triangulating a plant cell according to claim 5, wherein, First, assign each point of the plane with less points an initial value Then, loop Next, calculate the wire insertion points. The calculation method of the wire insertion points is: Wherein The function represents rounding the result, is the iteration variable in the loop.

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