Three-dimensional displays using electromagnetic field computations
Methods, apparatus, devices, and systems for three-dimensional (3D) displaying objects are provided. In one aspect, a method includes obtaining data including respective primitive data for primitives corresponding to an object, determining an electromagnetic (EM) field contribution to each element of a display for each of the primitives by calculating an EM field propagation from the primitive to the element, generating a sum of the EM field contributions from the primitives for each of the elements, transmitting to each of the elements a respective control signal for modulating at least one property of the element based on the sum of the EM field contributions, and transmitting a timing control signal to an illuminator to activate the illuminator to illuminate light on the display, such that the light is caused by the modulated elements of the display to form a volumetric light field corresponding to the object.
1. A method comprising:
for each of a plurality of primitives corresponding to an object, determining an electromagnetic (EM) field contribution to each of a plurality of elements of a display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the element;
for each of the plurality of elements, generating a sum of the EM field contributions from the plurality of primitives to the element, wherein a first primitive adjacent to a second primitive in the plurality of primitives is scaled by a predetermined factor such that a reconstruction of the first primitive does not overlap with a reconstruction of the second primitive; and
transmitting a timing control signal to an illuminator, the timing control signal indicating to turn on the illuminator such that the illuminator emits light on the display,
wherein:
the elements of the display cause the light to propagate in different directions to form a volumetric light field corresponding to the object in a 3D space, and
the volumetric light field corresponds to a solution of Maxwell's equations with a boundary condition defined by modulated elements of the display.
2. The method of claim 1 , wherein the predetermined factor is determined at least partially based on a resolution of the display.
3. The method of claim 1 , further comprising:
obtaining respective primitive data for each of the plurality of primitives, wherein the respective primitive data of each of the plurality of primitives comprises respective coordinate information of the primitive in the 3D coordinate system; and
determining new respective coordinate information of the first primitive based on the respective coordinate information of the first primitive and the predetermined factor.
4. The method of claim 3 , further comprising determining an EM field contribution from the first primitive to each of the plurality of elements based on the new respective coordinate information of the first primitive.
5. The method of claim 1 , further comprising scaling the second primitive by the predetermined factor.
6. The method of claim 1 , wherein:
the first primitive and the second primitive share a common part; and
the method comprises scaling the first primitive by scaling the common part of the first primitive.
7. The method of claim 1 , further comprising scaling the first primitive by the predetermined factor in a predetermined direction.
8. The method of claim 1 , further comprising, for each of the plurality of elements, generating a respective control signal based on the sum of the EM field contributions from the plurality of primitives to the element, the respective control signal being for modulating at least one property of the element based on the sum of the EM field contributions from the plurality of primitives to the element.
9. The method of claim 8 , wherein the at least one property of the element comprises at least one member selected from the group consisting of a refractive index, an amplitude index, a birefringence, and a retardance.
10. The method of claim 8 , wherein the respective control signal comprises an electrical signal, an optical signal, a magnetic signal, or an acoustic signal.
11. The method of claim 1 , wherein the timing control signal is transmitted in response to determining a completion of obtaining the sum of the field contributions for each of the plurality of elements.
12. The method of claim 1 , wherein the light comprises a white light, and the display is configured to diffract the white light into light with different colors.
13. A device comprising:
one or more processors; and
a non-transitory computer readable storage medium in communication with the one or more processors and storing instructions executable by the one or more processors and upon such execution cause the one or more processors to perform operations comprising:
for each of a plurality of primitives corresponding to an object, determining an electromagnetic (EM) field contribution to each of a plurality of elements of a display by computing, in a three-dimensional (3DB coordinate system, EM field propagation from the primitive to the element;
for each of the plurality of elements, generating a sum of the EM field contributions from the plurality of primitives to the element, wherein a first primitive adjacent to a second primitive in the plurality of primitives is scaled by a predetermined factor such that a reconstruction of the first primitive does not overlap with a reconstruction of the second primitive; and
transmitting a timing control signal to an illuminator, the timing control signal indicating to turn on the illuminator such that the illuminator emits light on the display,
wherein:
the elements of the display cause the light to propagate in different directions to form a volumetric light field corresponding to the object in a 3D space, and
the volumetric light field corresponds to a solution of Maxwell's equations with a boundary condition defined by modulated elements of the display.