Holographically displaying three-dimensional objects
Methods, apparatus, devices, subsystems, and systems for holographically displaying three-dimensional objects are provided. In one aspect, a method includes: obtaining primitive data of a plurality of primitives corresponding to an object, and adjusting the primitive data of the plurality of primitives to generate a gap between adjacent primitives of the plurality of primitives.
1. A method comprising:
obtaining primitive data of a plurality of primitives corresponding to an object; and
adjusting the primitive data of the plurality of primitives to generate a gap between adjacent primitives of the plurality of primitives.
2. The method of claim 1 , wherein, for at least one of a pair of adjacent primitives, the gap is no smaller than a predetermined value, and wherein, before the adjusting, the adjacent primitives are in contact and have at least one shared edge.
3. The method of claim 1 , wherein adjusting the primitive data of the plurality of primitives corresponding to the object to generate the gap between the adjacent primitives of the plurality of primitives comprises:
for each primitive of the adjacent primitives, shrinking the primitive by a half of the gap towards a center of the primitive.
4. The method of claim 3 , wherein coordinate information of the center of the primitive in a three-dimensional (3D) coordinate system remains unchanged, and a perpendicular distance between an edge of the primitive and the center of the primitive is decreased by the half of the gap.
5. The method of claim 3 , wherein coordinate data of the center of the primitive in a 3D coordinate system remain unchanged, and coordinate data of vertices defining the primitive are adapted with respect to the center of the primitive to create the gap.
6. The method of claim 1 , wherein adjusting the primitive data of the plurality of primitives corresponding to the object to generate the gap between the adjacent primitives of the plurality of primitives comprises:
scaling a shared edge of a first primitive adjacent to a second primitive; and
updating respective primitive data for the first primitive based on a result of the scaling.
7. The method of claim 6 , wherein scaling the shared edge of the first primitive adjacent to the second primitive comprises:
moving two vertices of the shared edge of the first primitive towards at least one adjacent vertex of the first primitive.
8. The method of claim 6 , wherein the first primitive has only one neighboring primitive that is the second primitive, and
wherein one or more other edges of the first primitive remain unscaled.
9. The method of claim 1 , further comprising:
receiving an input to generate the gap among the plurality of primitives,
wherein adjusting the primitive data of the plurality of primitives corresponding to the object to generate the gap between the adjacent primitives of the plurality of primitives is in response to receiving the input.
10. The method of claim 1 , wherein at least one of the plurality of primitives comprises a triangle primitive or a polygon primitive.
11. The method of claim 1 , wherein primitive data of a primitive comprises at least one of:
texture information of the primitive,
shading information on one or more surfaces of the primitive,
color information of the primitive, or coordinate information of the primitive in a 3D coordinate system.
12. The method of claim 1 , further comprising:
generating the primitive data of the plurality of primitives based on scene data of the object using a 3D simulation application, the scene data comprising information of the plurality of primitives.
13. A method, comprising:
obtaining primitive data of a plurality of primitives corresponding to an object, wherein the primitive data indicates a gap between adjacent primitives of the plurality of primitives;
for each of the plurality of primitives, determining an electromagnetic (EM) field contribution to each of a plurality of display elements of a display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element using primitive data of the primitive and coordinate data of the display element; and
for each of the plurality of display elements, generating a sum of the EM field contributions from each of the plurality of primitives to the display element.
14. The method of claim 13 , further comprising:
transmitting a respective control signal to each of the plurality of display elements of the display to modulate at least one property of the display element based on the sum of EM field contributions to the display element.
15. The method of claim 14 , further comprising:
illuminating light on modulated display elements of the display to form a volumetric light field in a three-dimensional (3D) space, the volumetric light field corresponding to a reconstruction of the object,
wherein the reconstruction of the object comprises reconstructed adjacent primitives corresponding to the adjacent primitives with the gap.
16. The method of claim 15 , wherein the gap is configured to make the reconstructed adjacent primitives be resolvable from each other.
17. The method of claim 15 , wherein the gap is configured to be small enough to make the reconstructed adjacent primitives appear seamless and to be big enough such that there is no overlap between the reconstructed adjacent primitives.
18. The method of claim 13 , wherein the gap is configured to be identical to or greater than a predetermined diffraction limit of the display.
19. The method of claim 18 , wherein a ratio between the gap and the predetermined diffraction limit of the display is in a range from 1 to 10.
20. The method of claim 18 , wherein the predetermined diffraction limit of the display is in accordance with Rayleigh Criterion.
21. The method of claim 20 , wherein the predetermined diffraction limit of the display is based on a size of a display element of the display and a wavelength of light to be incident on the display.
22. The method of claim 20 , wherein the predetermined diffraction limit of the display is expressed as:
res
=
0.61
tan
θ
o
where res represents the predetermined diffraction limit of the display, and θ o represents an output angle from a surface of the display.
23. The method of claim 22 , wherein the display comprises a cover on top of the plurality of display elements of the display, and
wherein the output angle θ o is expressed as:
θ
o
=
asin
(
n
i
n
o
*
sin
θ
i
)
and
θ
i
=
asin
(
λ
i
Λ
)
,
where θ i represents an incident angle on an interface between the cover and a surrounding medium, n i and n o represent a refractive index of a material of the cover and a refractive index of the surrounding medium, λ i represents a wavelength of light in the material of the cover, and Λ represents a display element period of the display.
24. The method of claim 23 , wherein the display element period of the display is one of
a period along a first direction of the display element of the display, or
a period along a second direction of the display element of the display that is perpendicular to the first direction.
25. A method, comprising:
obtaining primitive data of a plurality of primitives corresponding to an object;
adjusting the primitive data of the plurality of primitives to generate a gap between adjacent primitives of the plurality of primitives;
generating control signals for a plurality of display elements of a display using the adjusted primitive data of the plurality of primitives;
modulating the plurality of display elements of the display based on the control signals; and
illuminating light on modulated display elements of the display to form a volumetric light field in a three-dimensional (3D) space, the volumetric light field corresponding to a reconstruction of the object,
wherein the reconstruction of the object comprises reconstructed adjacent primitives corresponding to the adjacent primitives with the gap, and
wherein the gap is configured to make the reconstructed adjacent primitives be resolvable from each other.
26. The method of claim 25 , wherein the gap is configured to be small enough to make the reconstructed adjacent primitives appear seamless and great enough to make no overlap between the reconstructed adjacent primitives.
27. The method of claim 25 , wherein generating the control signals for the plurality of display elements of the display using the adjusted primitive data of the plurality of primitives comprises:
for each of the plurality of primitives, determining an electromagnetic (EM) field contribution to each of the plurality of display elements of the display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element using adjusted primitive data of the primitive and coordinate data of the display element, and
for each of the plurality of display elements, generating a sum of the EM field contributions from each of the plurality of primitives to the display element, and generating a respective control signal based on the sum of the EM field contributions for the display element.
28. The method of claim 25 , further comprising:
generating scene data of the object using a 3D simulation application; and
generating the primitive data of the plurality of primitives based on the scene data of the object, the scene data comprising information of the plurality of primitives.
29. The method of claim 25 , wherein the gap is configured to be identical to or greater than a predetermined diffraction limit of the display in accordance with Rayleigh Criterion.
30. A system, comprising:
a display; and
a controller coupled to the display,
wherein the controller is configured to:
obtain primitive data of a plurality of primitives corresponding to an object, wherein the primitive data indicates a gap between adjacent primitives of the plurality of primitives;
for each of the plurality of primitives, determine an electromagnetic (EM) field contribution to each of a plurality of display elements of the display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element using primitive data of the primitive and coordinate data of the display element;
for each of the plurality of display elements, generate a sum of the EM field contributions from each of the plurality of primitives to the display element;
generate control signals for the plurality of display elements of the display using sums of the EM field contributions for the plurality of display elements; and
transmit the control signals to the display to modulate the plurality of display elements of the display based on the control signals.