Generation of electrically enabled, doubly curved surfaces

1 . A system for generating instructions for a tool path for an electrically enabled, doubly curved surface, the system comprising:

at least one processor; and

one or more non-transitory computer-readable media storing computer-executable instructions that, when executed by the at least one processor, perform a method for generating the instructions for the tool path for the electrically enabled, doubly curved surface, the method comprising:

generating a 2-dimensional design of a unit cell design;

generating a point cloud array associated with the 2-dimensional design of the unit cell design,

wherein the point cloud array comprises a plurality of points;

generating the electrically enabled, doubly curved surface associated with the point cloud array, wherein generating the electrically enabled, doubly curved surface comprises:

determining a polar coordinate for each point of the plurality of points from the point cloud array such that a set of polar coordinates is obtained;

determining an absolute value of a radial distance of each polar coordinate from the set of polar coordinates;

normalizing the absolute value of the radial distance of each polar coordinate from the set of polar coordinates to obtain a set of normalized polar coordinates; and

interpolating the set of normalized polar coordinates to obtain the electrically enabled, doubly curved surface; and

generating the instructions for the tool path associated with the electrically enabled, doubly curved surface.

2 . The system of claim 1 , further comprising:

a 5-axis printer system operable to print the electrically enabled, doubly curved surface through deposition of a material on a printing surface,

wherein the printing surface comprises a tool movable about five axes, the tool being at least one of the printing surface or a print head; and

wherein the method further comprises:

executing, via the 5-axis printer system, the instructions for the tool path,

wherein the instructions comprise an instruction for a movement of the tool.

3 . The system of claim 2 ,

wherein the instructions for the tool path further comprise a shutter-off instruction preventing execution of the instruction for the movement of the tool.

4 . The system of claim 1 ,

wherein generating the instructions for the tool path associated with the electrically enabled, doubly curved surface comprises:

generating the instructions by at least:

for each point in a set of points of the electrically enabled, doubly curved surface, generating an instruction to move a tool of a printer system to the point;

identifying at least one instruction from the instructions moving the tool of the printer system to a predefined origin point; and

responsive to identifying the at least one instruction, overriding the at least one instruction from the instructions.

5 . The system of claim 4 ,

wherein overriding the at least one instruction from the instructions comprises:

removing the at least one instruction from the instructions.

6 . The system of claim 1 ,

wherein determining the polar coordinate for each point of the plurality of points comprises:

determining the radial distance, an azimuth angle, and a polar angle for each point of the plurality of points,

wherein each point from the plurality of points is converted to the polar coordinate from a Cartesian coordinate.

7 . The system of claim 6 ,

wherein the radial distance for each point of the plurality of points is based on a radial line between said point and an origin point, where the origin point is a center point of the electrically enabled, doubly curved surface.

8 . One or more non-transitory computer-readable media storing computer-executable instructions that, when executed by at least one processor, perform a method for generating instructions for a tool path for an electrically enabled, doubly curved surface, the method comprising:

generating a 2-dimensional design of a unit cell design,

wherein the 2-dimensional design comprises a plurality of points along a singular line;

generating the electrically enabled, doubly curved surface associated with the 2-dimensional design, wherein generating the electrically enabled, doubly curved surface comprises:

determining a polar coordinate for each point of the plurality of points from the 2-dimensional design such that a set of polar coordinates is obtained;

determining an absolute value of a radial distance of each polar coordinate from the set of polar coordinates;

normalizing the absolute value of the radial distance of each polar coordinate from the set of polar coordinates to obtain a set of normalized polar coordinates; and

interpolating the set of normalized polar coordinates to obtain the electrically enabled, doubly curved surface; and

generating the instructions for the tool path associated with the electrically enabled, doubly curved surface.

9 . The one or more non-transitory computer-readable media of claim 8 ,

wherein generating the instructions for the tool path associated with the electrically enabled, doubly curved surface comprises:

obtaining the instructions by at least:

for each point in a set of points of the electrically enabled, doubly curved surface, generating an instruction to at least one of:

deposit ink between the point and an adjacent point in the set of points; or

move a tool of a printer system to the point.

10 . The one or more non-transitory computer-readable media of claim 9 ,

wherein generating the instructions for the tool path associated with the electrically enabled, doubly curved surface further comprises:

identifying at least one instruction from the instructions where the adjacent point is a predefined origin point; and

responsive to identifying the at least one instruction, generating a shutter off instruction such that the tool of the printer system is prevented from depositing the ink between the point and the predefined origin point.

11 . The one or more non-transitory computer-readable media of claim 8 ,

wherein generating the 2-dimensional design of the unit cell design further comprises:

selectively designing the 2-dimensional design to reflect a predetermined range of frequencies when printed on a nonplanar surface.

12 . The one or more non-transitory computer-readable media of claim 8 ,

wherein the method further comprises:

transmitting the instructions for the tool path to a multi-axis printer system, wherein the multi-axis printer system is operable to execute the instructions for the tool path to print the electrically enabled, doubly curved surface on a curved printing surface of the multi-axis printer system.

13 . The one or more non-transitory computer-readable media of claim 12 ,

wherein the instructions for the tool path comprise:

a shutter-off instruction such that the multi-axis printer system overrides a subsequent instruction based on the shutter-off instruction.

14 . The one or more non-transitory computer-readable media of claim 13 ,

wherein the subsequent instruction comprises a print head of the multi-axis printer system returning to an origin point of the electrically enabled, doubly curved surface.

15 . A method for generating instructions for a tool path for an electrically enabled, doubly curved surface, the method comprising:

generating a 2-dimensional design of a unit cell design;

generating a point cloud array associated with the 2-dimensional design of the unit cell design,

wherein the point cloud array comprises a plurality of points;

generating the electrically enabled, doubly curved surface associated with the point cloud array, wherein generating the electrically enabled, doubly curved surface comprises:

determining a polar coordinate for each point of the plurality of points from the point cloud array such that a set of polar coordinates is obtained;

determining an absolute value of a radial distance of each polar coordinate from the set of polar coordinates;

normalizing the absolute value of the radial distance of each polar coordinate from the set of polar coordinates to obtain a set of normalized polar coordinates; and

interpolating the set of normalized polar coordinates to obtain the electrically enabled, doubly curved surface; and

generating the instructions for the tool path associated with the electrically enabled, doubly curved surface.

16 . The method of claim 15 ,

wherein generating the 2-dimensional design of the unit cell design comprises:

generating a repeatable pattern of the unit cell design across the 2-dimensional design,

wherein the unit cell design is selectively shaped to reflect a predetermined range of frequencies.

17 . The method of claim 16 ,

wherein interpolating the set of normalized polar coordinates to obtain the electrically enabled, doubly curved surface comprises:

performing at least one of linear interpolation or bilinear interpolation of the set of normalized polar coordinates across a sphere.

18 . The method of claim 17 , further comprising:

wherein a shape of the 2-dimensional design of the unit cell design is selectively chosen for compatibility with one or more tools of a multi-axis printer system,

wherein the shape of the 2-dimensional design of the unit cell design is circular.

19 . The method of claim 15 ,

wherein the point cloud array is ordered such that an origin point of the point cloud array is a first point in the point cloud array,

wherein the origin point is a central point of the 2-dimensional design of the unit cell design.

20 . The method of claim 15 , further comprising:

printing, via a multi-axis printer system, a plurality of frequency selective surfaces, including the electrically enabled, doubly curved surface based on the instructions for the tool path to obtain a plurality of printed frequency selective surfaces; and

coupling the plurality of printed frequency selective surfaces together to form a truncated icosahedron.