Three-dimensional shape conversion system, three-dimensional shape conversion method, and program for conversion of three-dimensional shape

• US 20090040224A1
• Filed: 02/01/2008
• Published: 02/12/2009
• Est. Priority Date: 08/06/2007
• Status: Abandoned Application

• Current Assignee: University of Tokyo
• Original Assignee: University of Tokyo
• Inventors: Mori, Yuki, Igarashi, Takeo
• Application Number:
  US12/068,075
• Publication Number:
  US 20090040224A1
• Time in Patent Office: Days
• US Class Current: 345/427
• CPC Class Codes: G06T 19/00 Manipulating 3D models or images for computer graphics
• CPC Class Codes: G06T 2219/021 Flattening

Abstract

In a computer 20 with a three-dimensional shape conversion program installed therein, a coordinate processing unit 21 obtains two-dimensional coordinate data of a contour stroke SS input through the user'"'"'s operation of a mouse 50 or another suitable input unit. A 2D/3D modeling unit 22 performs two-dimensional modeling based on the obtained two-dimensional coordinate data and thereby generates two-dimensional model data regarding a two-dimensional pattern, while performing three-dimensional modeling based on the generated two-dimensional model data and generates three-dimensional model data regarding a three-dimensional shape obtained by expanding the two-dimensional pattern. A 2D model data regulator 23 adjusts the two-dimensional model data to make a corresponding contour of the three-dimensional shape defined by the three-dimensional model data substantially consistent with the input contour stroke SS.

Claims

1. A three-dimensional shape conversion system constructed to convert a three-dimensional shape into two dimensions, the three-dimensional shape conversion system comprising:

an input unit configured to input a contour of a three-dimensional shape;

a coordinate acquisition module configured to obtain two-dimensional coordinate data of the contour input via the input module;

a two-dimensional modeling module configured to perform two-dimensional modeling based on the obtained two-dimensional coordinate data and thereby generate two-dimensional model data regarding a two-dimensional pattern defined by the two-dimensional coordinate data;

a three-dimensional modeling module configured to perform three-dimensional modeling based on the generated two-dimensional model data and thereby generate three-dimensional model data regarding a three-dimensional shape obtained by expanding the two-dimensional pattern defined by the two-dimensional model data; and

a two-dimensional model data regulator configured to adjust the generated two-dimensional model data, in order to make a corresponding contour of the three-dimensional shape defined by the three-dimensional model data substantially consistent with the input contour.

2. The three-dimensional shape conversion system in accordance with claim 1, wherein the adjustment of the two-dimensional model data by the two-dimensional model data regulator and update of the three-dimensional model data based on the adjusted two-dimensional model data by the three-dimensional modeling module are repeated until the corresponding contour of the three-dimensional shape defined by the three-dimensional model data becomes basically consistent with the input contour.

3. The three-dimensional shape conversion system in accordance with claim 1, wherein the two-dimensional modeling module generates two-dimensional model data with regard to a pair of two-dimensional patterns as two opposed sides relative to the input contour, and the three-dimensional modeling module generates three-dimensional model data regarding a three-dimensional shape obtained by expanding the pair of two-dimensional patterns with joint of corresponding outer circumferences.

4. The three-dimensional shape conversion system in accordance with claim 1, wherein the coordinate acquisition module obtains two-dimensional coordinate data of each tentative vertex included in the corresponding contour of the three-dimensional shape defined by the three-dimensional model data in a predetermined two-dimensional coordinate system, and

the two-dimensional model data regulator includes:

a projection component length computation module configured to compute a projection component length of each vector, which connects each target vertex included in the input contour with a corresponding tentative vertex corresponding to the target vertex, in a normal direction of the tentative vertex, based on two-dimensional coordinate data of the tentative vertex and the target vertex; and

a coordinate computation module configured to compute coordinates of each object vertex included in a contour of the two-dimensional pattern defined by the two-dimensional model data after a motion of the object vertex in a normal direction of the object vertex by the computed projection component length.

5. The three-dimensional shape conversion system in accordance with claim 4, the three-dimensional shape conversion system further including:

a detection module configured to compare a sum of the projection component lengths with regard to all the tentative vertexes with a preset reference value and, when the sum becomes not greater than the preset reference value, detect a consistency of the corresponding contour of the three-dimensional shape defined by the three-dimensional model data with the input contour.

6. The three-dimensional shape conversion system in accordance with claim 1, wherein the two-dimensional modeling module divides the two-dimensional pattern defined by the two-dimensional coordinate data of the input contour into polygon meshes, and outputs coordinates of respective vertexes of the polygon meshes and length of each edge interconnecting each pair of the vertexes as the two-dimensional model data.

7. The three-dimensional shape conversion system in accordance with claim 6, wherein the three-dimensional modeling module computes coordinates of each vertex of the polygon meshes and the length of each edge interconnecting each pair of the vertexes based on the two-dimensional model data when a mesh plane formed by each edge of the polygon meshes is moved outward in a normal direction of the mesh plane under a predetermined moving restriction in the normal direction of the mesh plane and under a predetermined expansion-contraction restriction of restricting at least expansion of each edge of the polygon meshes, and outputs the computed coordinates and the computed length of each edge as the three-dimensional model data.

8. The three-dimensional shape conversion system in accordance with claim 7, wherein the predetermined moving restriction sets a moving distance Δ

df of a specific vertex Vi according to Equation (1) given below;

$\begin{array}{cc}\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{df}=\mathrm{\alpha <br><br>}·<br><br>\frac{\underset{f\in <br><br>\mathrm{Ni}}{\sum <br><br>}<br><br>A<br><br>\left(f\right)·<br><br>n<br><br>\left(f\right)}{\underset{f\in <br><br>N}{\sum <br><br>}<br><br>A<br><br>\left(f\right)}& \left(1\right)\end{array}$

where A(f), n(f), and Ni respectively denote an area of a mesh plane f, a normal vector of the mesh plane f, and a set of mesh planes including the specific vertex Vi, and a represents a preset coefficient,

the predetermined expansion-contraction restriction sets a moving distance Δ

de of the specific vertex Vi according to Equation (2) given below;

$\begin{array}{cc}\mathrm{\Delta <br><br>}<br><br><br><br>\mathrm{de}=\mathrm{\beta <br><br>}·<br><br>\frac{\underset{\mathrm{eij}\in <br><br>\mathrm{Ei}}{\sum <br><br>}<br><br>\left\{A<br><br>\left(e.\mathrm{leftface}\right)+A<br><br>\left(e.\mathrm{rightface}\right)\right\}·<br><br>t_{\mathrm{ij}}}{\underset{\mathrm{eij}\in <br><br>\mathrm{Ei}}{\sum <br><br>}<br><br>\left\{A<br><br>\left(e.\mathrm{leftface}\right)+A<br><br>\left(e.\mathrm{rightface}\right)\right\}}& \left(2\right)\end{array}$

where Vj, eij, Eij, A(e,leftface), A(e,rightface), and tij respectively denote a vertex connected with the specific vertex Vi by means of an edge, an edge interconnecting the specific vertex Vi with the vertex Vj, a set of edges eij intersecting the specific vertex Vi, an area of a plane located on the left of the edge eij, an area of a plane located on the right of the edge eij, and a pulling force applied from the edge eij to the vertexes Vi and Vj, β

represents a preset coefficient, and the pulling force tij is defined according to Equation (3) given below;

$\begin{array}{cc}{t}_{\mathrm{ij}}=\left\{\begin{array}{ccc}0.5·<br><br>\left(\mathrm{vj}-\mathrm{vi}\right)·<br><br>\frac{<br><br>\mathrm{vi}-\mathrm{vj}<br><br>-l_{\mathrm{ij}}}{<br><br>\mathrm{vi}-\mathrm{vj}<br><br>}& \mathrm{\dots <br><br>}& \mathrm{if}<br><br><br><br><br><br>\mathrm{vi}-\mathrm{vj}<br><br>\ge <br><br>l_{\mathrm{ij}}\\ 0& \mathrm{\dots <br><br>}& \mathrm{if}<br><br><br><br><br><br>\mathrm{vi}-\mathrm{vj}<br><br><<br><br>l_{\mathrm{ij}}\end{array}\right\}& \left(3\right)\end{array}$

where lij denotes an original edge length, and

the three-dimensional modeling module computes three-dimensional coordinate data when all vertexes Vi are moved by the moving distance Δ

df set according to Equation (1) given above and are further moved at least once by the moving distance Δ

de set according to Equation (2) given above.

9. The three-dimensional shape conversion system in accordance with claim 1, the three-dimensional shape conversion system further including:

a three-dimensional image display unit configured to display a three-dimensional image on a window thereof;

a two-dimensional image display unit configured to display a two-dimensional image on a window thereof;

a three-dimensional image display controller configured to control the three-dimensional image display unit to display a three-dimensional image representing the three-dimensional shape on the window, based on the three-dimensional model data; and

a two-dimensional image display controller configured to control the two-dimensional image display unit to display a two-dimensional image representing the two-dimensional pattern on the window, based on the two-dimensional model data generated by the two-dimensional modeling module or the two-dimensional model data adjusted by the two-dimensional model data regulator.

10. The three-dimensional shape conversion system in accordance with claim 9, wherein in response to an operation of the input unit for entry of a cutoff stroke that intersects an outer circumference of the three-dimensional image displayed on the window of the three-dimensional display unit at two different points and cuts off part of the three-dimensional image, the three-dimensional modeling module generates the three-dimensional model data to reflect a split of the three-dimensional shape defined by the three-dimensional model data by a developable surface obtained by sweep of the cutoff stroke in a specified direction to leave one side area of the developable surface remain but to eliminate the other side area of the developable surface, and

the two-dimensional model data regulator adjusts the two-dimensional model data corresponding to the remaining side area of the developable surface based on the generated three-dimensional model data.

11. The three-dimensional shape conversion system in accordance with claim 10, wherein the three-dimensional modeling module generates three-dimensional model data regarding a three-dimensional shape obtained by expanding a two-dimensional pattern based on the two-dimensional model data adjusted corresponding to the remaining side area of the developable surface, and

the adjustment of the two-dimensional model data by the two-dimensional model data regulator and update of the three-dimensional model data based on the adjusted two-dimensional model data by the three-dimensional modeling module are repeated until a contour corresponding to the cutoff stroke in the three-dimensional shape by the generated three-dimensional model data becomes basically consistent with the input cutoff stroke.

12. The three-dimensional shape conversion system in accordance with claim 9, wherein in response to an operation of the input unit for entry of an additional stroke that has a starting point and an end point on or inside of an outer circumference of the three-dimensional image displayed on the window of the three-dimensional display unit and is protruded outward from the outer circumference of the three-dimensional image, the three-dimensional modeling module generates the three-dimensional model data to reflect formation of a predetermined baseline passing through the starting point and the end point of the input additional stroke,

the coordinate acquisition module obtains two-dimensional coordinate data of a vertex included in the additional stroke in a predetermined two-dimensional coordinate system set on a preset virtual plane including the starting point and the endpoint of the additional stroke, while obtaining two-dimensional coordinate data of a vertex included in the baseline in projection onto the virtual plane, and

the two-dimensional model data regulator adjusts the two-dimensional model data corresponding to the additional stroke and the baseline, based on the obtained two-dimensional coordinate data of the vertex included in the additional stroke and the obtained two-dimensional coordinate data of the vertex included in the baseline.

13. The three-dimensional shape conversion system in accordance with claim 12, wherein the baseline is a line included in a line of intersection between a surface of the three-dimensional shape and the virtual plane and extended from the starting point to the end point of the additional stroke.

14. The three-dimensional shape conversion system in accordance with claim 12, wherein the baseline is a closed line including the starting point and the endpoint of the additional stroke and forming a predetermined planar shape.

15. The three-dimensional shape conversion system in accordance with claim 12, wherein the three-dimensional modeling module generates three-dimensional model data regarding a three-dimensional shape obtained by expanding a two-dimensional pattern based on the two-dimensional model data adjusted corresponding to the additional stroke and the baseline, and

the adjustment of the two-dimensional model data by the two-dimensional model data regulator and update of the three-dimensional model data based on the adjusted two-dimensional model data by the three-dimensional modeling module are repeated until a contour corresponding to the additional stroke in the three-dimensional shape defined by the three-dimensional model data becomes basically consistent with the input additional stroke.

16. The three-dimensional shape conversion system in accordance with claim 9, the three-dimensional shape conversion system further including:

a three-dimensional image manipulation unit operated to move a movable vertex, which is a vertex included in a seam line corresponding to connection lines of multiple two-dimensional patterns, on the window of the three-dimensional image display unit,

wherein the coordinate acquisition module obtains two-dimensional coordinate data of the movable vertex in a predetermined two-dimensional coordinate system set on a preset virtual plane based on the movable vertex and the seam line including the movable vertex, when the movable vertex is moved on the window of the three-dimensional image display unit by an operation of the three-dimensional image manipulation unit,

the two-dimensional model data regulator calculates a moving distance of the movable vertex on the virtual plane based on the two-dimensional coordinate data, and adjusts the two-dimensional model data to reflect a motion of a specific vertex, which is included in the connection lines and corresponds to the movable vertex, in a normal direction of the specific vertex by the calculated moving distance, and

the three-dimensional modeling module updates the three-dimensional model data based on the adjusted two-dimensional model data.

17. The three-dimensional shape conversion system in accordance with claim 9, the three-dimensional shape conversion system further including:

a two-dimensional image manipulation unit operated to move a movable vertex, which is a vertex included in an outer circumference of the two-dimensional pattern, on the window of the two-dimensional image display unit,

wherein the coordinate acquisition module obtains two-dimensional coordinate data of the movable vertex in a predetermined two-dimensional coordinate system, when the movable vertex is moved on the window of the two-dimensional image display unit by an operation of the two-dimensional image manipulation unit,

the two-dimensional model data regulator adjusts the two-dimensional model data to reflect a motion of the movable vertex from its original position to a position specified by the obtained two-dimensional coordinate data, and

the three-dimensional modeling module updates the three-dimensional model data based on the adjusted two-dimensional model data.

18. The three-dimensional shape conversion system in accordance with claim 9, wherein in response to an operation of the input unit for entry of a cutting stroke that has a starting point and an end point on or inside of an outer circumference of the three-dimensional image displayed on the window of the three-dimensional image display unit and is wholly located inside the outer circumference of the three-dimensional image, the three-dimensional modeling module updates the three-dimensional model data to reflect formation of a cutting line at a position corresponding to the cutting stroke, and

the two-dimensional model data regulator adjusts the two-dimensional model data based on the updated three-dimensional model data.

19. A three-dimensional shape conversion method of converting a three-dimensional shape into two dimensions, the three-dimensional shape conversion method comprising the steps of:

(a) obtaining two-dimensional coordinate data of a contour of a three-dimensional shape input by an operation of an input unit;

(b) performing two-dimensional modeling based on the obtained two-dimensional coordinate data and thereby generating two-dimensional model data regarding a two-dimensional pattern defined by the two-dimensional coordinate data;

(c) performing three-dimensional modeling based on the generated two-dimensional model data and thereby generating three-dimensional model data regarding a three-dimensional shape obtained by expanding the two-dimensional pattern defined by the two-dimensional model data; and

(d) adjusting the generated two-dimensional model data, in order to make a corresponding contour of the three-dimensional shape defined by the three-dimensional model data substantially consistent with the input contour.

20. The three-dimensional shape conversion method in accordance with claim 19, wherein the step (d) of adjusting the two-dimensional model data and step (e) of updating the three-dimensional model data based on the two-dimensional model data adjusted in the step (d) are repeated until the corresponding contour of the three-dimensional shape defined by the three-dimensional model data becomes basically consistent with the input contour.

21. A three-dimensional shape conversion program executed to enable a computer to function as a three-dimensional shape conversion system of converting a three-dimensional shape into two dimensions, the three-dimensional shape conversion program comprising:

a coordinate acquisition module configured to obtain two-dimensional coordinate data of a contour of a three-dimensional shape input by an operation of an input unit;

a two-dimensional modeling module configured to perform two-dimensional modeling based on the obtained two-dimensional coordinate data and thereby generate two-dimensional model data regarding a two-dimensional pattern defined by the two-dimensional coordinate data;

a three-dimensional modeling module configured to perform three-dimensional modeling based on the generated two-dimensional model data and thereby generate three-dimensional model data regarding a three-dimensional shape obtained by expanding the two-dimensional pattern defined by the two-dimensional model data; and

a two-dimensional model data adjustment module configured to adjust the generated two-dimensional model data, in order to make a corresponding contour of the three-dimensional shape defined by the three-dimensional model data substantially consistent with the input contour.