Deposition of non-uniform non-overlapping curvilinear segments of anisotropic filament to form non-uniform layers
A process of additive manufacturing in which a stack of non-planar layers of material are deposited for manufacturing an object. The non-planar layers can conform to the surface of the object or not. The non-planar layers can create structurally-advantageous interior structures in the object. The contours of the non-planar layers can be different or can be the same.
1. An article of manufacture comprising:
a first layer DL[n] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the first layer DL[n] is bounded by a first surface z=s(x,y,n) and a second surface z=s(x,y,n+1);
wherein s(u,v,n+1)−s(x,y,n)≠constant for all x,y, wherein s(u,v,n+1) is a point on the second surface that intersects a vector that is normal to the first surface at s(x,y,n); and
wherein n is an integer, x and u are real numbers in the domain x,u: [x S <x L ], y and v are real numbers in the domain y,v: [y S <y L ], z is a real number in the range z: [z S <z L ].
2. The article of manufacture of claim 1 wherein s(u 1 ,v 1,n+ 1)−s(x 1 ,y 1 ,n) is a first extrema; and
wherein x 1 and y 1 are real numbers, x S <x 1 <x L , and y S <y 1 <y L .
3. The article of manufacture of claim 2 wherein s(u 2 ,v 2 ,n+1)−s(x 2 ,y 2 ,n) is a second extrema; and
wherein x 2 and y 2 are real numbers, x S <x 1 <x 2 <x L , and y S <y 1 <y 2 <y L .
4. The article of manufacture of claim 3 wherein the first extrema is a first local maxima and the second extrema is a second local maxima.
5. The article of manufacture of claim 3 wherein the first extrema is a first local minima and the second extrema is a second local minima.
6. The article of manufacture of claim 3 wherein the first extrema is a first local maxima and the second extrema is a first local minima.
7. An article of manufacture comprising:
a first layer DL[n] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the first layer DL[n] is bounded by a first surface z=s(x,y,n) and a second surface z=s(x,y,n+1);
a second layer DL[n+1] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the second layer DL[n+1 ]is bounded by the second surface z=s(x,y,n+1) and a third surface z=s(x,y,n+2);
wherein s(u 1 ,v 1 ,n+1)−s(x 1 ,y 1 ,n) is a first extrema, wherein s(u 1 ,v 1 ,n+1) is the a first point on the second surface that intersects a vector that is normal to the first surface at s(x 1 ,y 1 ,n);
wherein s(u 2 ,v 2 ,n+2)−s(x 2 ,y 2 ,n+1) is a second extrema, wherein s(u 2 ,v 2 ,n+2) is a second point on the third surface that intersects a vector that is normal to the second surface at s(x 2 ,y 2 ,n+1);
wherein s(u 3 ,v 3 ,n+1)−s(x 3 ,y 3 ,n) is a third extrema, wherein s(u 3 ,v 3 ,n+1) is a third point on the second surface that intersects a vector that is normal to the first surface at s(x 3 ,y 3 ,n);
wherein s(u 4 ,v 4 ,n+2)−s(x 4 ,y 4 ,n+1) is a fourth extrema, wherein s(u 4 ,v 4 ,n+2) is a fourth point on the third surface that intersects a vector that is normal to the second surface at s(x 4 ,y 4 ,n+1); and
wherein n is an integer, x,x 1 ,x 2 ,x 3 ,x 4 ,u 1 ,u 2 ,u 3 , and u 4 are real numbers in the domain x: [x S <x 1 ,x 2 ,x 3 ,x 4 ,u 1 ,u 2 ,u 3 ,u 4 <x L ],y,y 1 ,y 2 ,y 3 ,y 4 ,v 1 ,v 2 ,v 3 , and v 4 are real numbers in the domain y: [y S <y 1 ,y 2 ,y 3 ,y 4 ,v 1 ,v 2 ,v 3 ,v 4 <y L ], and z is a real number in the range z: [z S <z L ].
8. The article of manufacture of claim 7 wherein x 1 =x 2 ,x 3 =x 4 ,y 1 =y 2 , and y 3 =y 4 .
9. The article of manufacture of claim 7 wherein x 1 >x 2 ,x 3 =x 4 ,y 1 =y 2 , and y 3 =y 4 .
10. The article of manufacture of claim 7 wherein x 1 >x 2 , x 3 >x 4 ,y 1 >y 2 , and y 3 >y 4 .
11. The article of manufacture of claim 7 wherein x 1 >x 2 , x 3 <x 4 ,y 1 >y 2 , and y 3 <y 4 .
12. The article of manufacture of claim 7 wherein the first extrema is a first local maxima and the third extrema is a second local maxima.
13. The article of manufacture of claim 7 wherein the first extrema is a first local minima and the third extrema is a second local minima.
14. The article of manufacture of claim 7 wherein the first extrema is a first local maxima and the third extrema is a first local minima.
15. An article of manufacture comprising:
a first layer DL[n] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the first layer DL[n] is bounded by a first surface z=s(x,y,n) and a second surface z=s(x,y,n+1);
a second layer DL[n+1] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the second layer DL[n+1] is bounded by the second surface z=s(x,y,n+1) and a third surface z=s(x,y,n+2);
wherein s(u 1 ,v 1 ,n+1)−s(x 1 ,y 1 ,n) is a first extrema, wherein s(u 1 ,v 1 ,n+1) is a second point on the second surface that intersects a vector that is normal to the first surface at s(x 1 ,y 1 ,n);
wherein s(u 2 ,v 2 ,n+2)−s(x 1 ,y 1 ,n+1) is a second extrema, wherein s(u 2 ,v 2 ,n+2) is a third point on the third surface that intersects a vector that is normal to the second surface at s(x 1 ,y 1 ,n+1); and
wherein n is an integer, x,x 1 ,u 1 , and u 2 are real numbers in the domain x: [x S <x 1 ,u 1 ,u 2 <x L ], y,y 1 ,v 1 , and v 2 are real numbers in the domain y: [y S <y 1 ,v 1 ,v 2 <y L ], and z is a real number in the range z: [z S <z L ].
16. The article of manufacture of claim 15 wherein the first extrema is a first local maxima and the second extrema is a second local maxima.
17. The article of manufacture of claim 15 wherein the first extrema is a first local maxima and the second extrema is a first local minima.
18. The article of manufacture of claim 15 wherein the first extrema is a first local minima and the second extrema is a second local minima.
19. The article of manufacture of claim 15 further comprising:
a third layer DL[n+2] comprised of non-overlapping curvilinear segments of anisotropic filament, wherein the third layer DL[n+2] is bounded by the third surface z=s(x,y,n+2) and a fourth surface z=s(x,y,n+3);
wherein s(u 3 ,v 3 ,n+3)−s(x 1 ,y 1 ,n+2) is a third extrema, wherein s(u 3 ,v 3 ,n+3) is a fourth point on the fourth surface that intersects a vector that is normal to the third surface at s(x 1 ,y 1 ,n+2); and
wherein the first extrema is a first local maxima and the third extrema is a first local minima;
wherein u 3 is a real number in the domain x: [x S <u 3 <x L ], and v 3 is a real number in the domain y: [y S <v 3 <y L ].
20. The article of manufacture of claim 19 wherein the first extrema is a first local minima and the third extrema is a first local maxima.