Method for creating a curved covering from flat material
A method includes providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh. The three-dimensional surface is cut into one or more panels representing each panel by a triangulated mesh. A two-dimensional approximation of the set of panels is created by representing the two-dimensional pattern as a triangulated mesh that is topologically equivalent to the three-dimensional meshes representing the panels.
1. A method, comprising:
providing a three-dimensional representation of a doubly curved surface as a smooth function or triangulated mesh;
determining a map of principal curvatures of the three-dimensional representation of the double curved surface;
cutting a flat, developable surface into a set of panels, wherein each panel of the set of panels is represented by a three-dimensional triangulated mesh;
introducing cuts to the set of panels primarily oriented along a direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the double curved surface; and
creating a two-dimensional approximation of the set of panels by representing each panel of the set of panels as a triangulated mesh that is topologically equivalent to the three-dimensional triangulated meshes that represent each of the panels.
2. The method of claim 1 , wherein the cuts introduced to the set of panels include cuts that divide the set of panels separate panels or cuts that act as relief cuts for one or more panels of the set of panels.
3. The method of claim 1 , wherein the cuts introduced to the set of panels are no more than a maximum number of relief cuts with respect to a desired level of fit of the developable surface to the doubly curved surface.
4. The method of claim 1 , wherein a number of panels of the set of panels are no more than a maximum number of panels with respect to a desired level of fit of the developable surface to the doubly curved surface.
5. The method of claim 1 , wherein the cuts are positioned on a line of the maximum principal curvature of the three-dimensional representation of the double curved surface.
6. The method of claim 1 , further comprising:
introducing additional cuts to the set of panels not oriented along the direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the double curved surface.
7. A method of creating a flat covering for a doubly curved surface, the method comprising:
determining a map of principal curvatures of a three-dimensional representation of the double curved surface;
cutting a flat, developable surface into a set of panels; and
introducing cuts to one or more panels of the set of panels,
wherein each of the introduced cuts are primarily oriented along a direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the double curved surface.
8. The method of claim 7 , wherein the cuts are positioned on a line of the maximum principal curvature of the three-dimensional representation of the double curved surface.
9. The method of claim 7 , wherein a number of introduced cuts is based on a desired level of fit of the developable surface to the doubly curved surface.
10. The method of claim 7 , further comprising:
introducing additional cuts to the set of panels,
wherein the additional cuts are oriented in a direction perpendicular to the direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the double curved surface.
11. The method of claim 7 , further comprising:
introducing additional cuts to the set of panels,
wherein the additional cuts are oriented in a direction different from the direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the double curved surface.
12. The method of claim 7 , wherein a cut is primarily oriented along the direction of maximum principal curvature when a dot product between a unit vector giving a direction of the cut and a unit vector giving the direction of the maximum principal curvature is greater than or equal to 0.7.
13. The method of claim 7 , wherein the doubly curved surface is a car window, and wherein the flat covering is applied to the car window.
14. A flat covering configured to be applied to a car window, the flat covering comprising:
multiple panels that combine to form a flat, developable surface to be applied to the car window,
wherein each panel of the multiple panels includes one or more relief cuts introduced to the panel,
wherein the relief cuts are primarily oriented along a direction of maximum principal curvature identified by a map of principal curvatures of a three-dimensional representation of the car window.
15. The flat covering of claim 14 , wherein at least one panel of the multiple panels includes an additional cut that is oriented in a direction perpendicular to the direction of maximum principal curvature identified by the map of principal curvatures of the three-dimensional representation of the car window.
16. The flat covering of claim 14 , wherein the relief cuts are positioned on a line of the maximum principal curvature of the three-dimensional representation of the car window.