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 display elements of a display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element based on a predetermined expression for a primitive type that the primitive belongs to, different primitive types corresponding to different predetermined expressions, wherein a primitive represents a geometric or a graphical element for input or output within a computing system and is defined by one or more vertices; 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.
2. The method of claim 1 , wherein the plurality of primitives comprise at least one member selected from the group consisting of a point primitive, a line primitive, and a polygon primitive.
3. The method of claim 1 , further comprising obtaining respective primitive data for each primitive of the plurality of primitives,
wherein the respective primitive data for the primitive comprises at least one member selected from the group consisting of:
texture information of the primitive;
shading information on one or more surfaces of the primitive;
color information of the primitive; and
coordinate information of the primitive in the 3D coordinate system.
4. The method of claim 1 , wherein determining the EM field contribution of the primitive to each display element of the plurality of display elements of the display comprises:
determining, in the 3D coordinate system, at least one distance between the display element and the primitive based on corresponding coordinate information of the display element and corresponding coordinate information of the primitive, and
determining the EM field contribution of the primitive to the display element based on a predetermined expression for the primitive and the at least one distance.
5. The method of claim 4 , wherein the predetermined expression is determined based on at least one of:
analytically calculating the EM field propagation from the primitive to the display element,
a solution of Maxwell's equations with a boundary condition defined by the display, or
at least one member selected from the group consisting of functions comprising a sine function, a cosine function, and an exponential function, wherein determining the EM field contribution comprises identifying a value of the at least one of the functions in a table stored in a memory.
6. The method of claim 1 , comprising:
determining first respective EM field contributions from a first primitive of the plurality of primitives to each display element of the plurality of display elements;
determining second respective EM field contributions from a second primitive of the plurality of primitives to each display element of the plurality of display elements; and
accumulating the EM field contributions for each display element of the plurality of display elements by adding the first and second respective EM field contributions corresponding to the display element.
7. The method of claim 1 , further comprising:
transmitting, for each of the plurality of display elements, a respective control signal to the display element, the control signal being for modulating at least one property of the display element based on the sum of the EM field contributions to the display element; 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 modulated elements of the display to form a volumetric light field corresponding to the object in a 3D space.
8. The method of claim 1 , comprising calculating a mathematical function using at least one of fixed point number representations or floating point number representations.
9. The method of claim 1 , comprising calculating respective EM field contributions of each primitive of the plurality of primitives to each display element of the plurality of display elements,
wherein the calculation of the respective EM field contributions is without at least one member selected from the group consisting of: expanding a geometry of the object into the plurality of display elements; applying visibility tests before packing wavefronts; and decision making or communication between parallel calculations for different primitives of the plurality of primitives; and
wherein the calculation of the respective EM field contributions is configured to cause at least one member selected from the group consisting of: tuning parallel calculations for multiple primitives to speed, cost, size or energy optimization; reducing latency between initiating a draw and a result being ready for display; increasing an accuracy using fixed point number representations; and optimizing computation speed by optimizing mathematical functions.
10. The method of claim 1 , further comprising:
obtaining respective primitive data of the plurality of primitives corresponding to the object;
scaling a first primitive adjacent to a second primitive by a predetermined factor using the respective primitive data for the first primitive and the second primitive; and
updating the respective primitive data for the first primitive based on a result of the scaling,
wherein the scaling is performed such that a gap between a reconstruction of the first and second primitives in a 3D space is big enough to separate the first and second primitives to minimize an overlapping effect and small enough to make the reconstruction appear seamless.
11. The method of claim 1 , comprising:
obtaining a plurality of discrete cosine transform (DCT) weights of an image to be mapped on a specified surface of one or more primitives of the plurality of primitives;
determining a respective EM field contribution of each of the one or more primitives to each display element of the plurality of display elements by taking into consideration of an effect of the plurality of DCT weights of the image;
decoding the DCT weights of the image to obtain a respective DCT amplitude for each pixel of the image; and
storing values associated with the respective DCT amplitudes of the pixels of the image together with primitive data of the one or more primitives,
wherein determining the respective EM field contribution comprises calculating the respective EM field contribution from each of the one or more primitives to each of the plurality of display elements with the values associated with the respective DCT amplitudes of the pixels of the image.
12. The method of claim 1 , comprising:
obtaining information of a given primitive and an occluder of the given primitive, wherein the given primitive is within the plurality of primitives corresponding to the object;
determining one or more particular display elements that make no contribution to a reconstruction of the given primitive at an effect of the occluder; and
for each of the one or more particular display elements, generating a respective sum of EM field contributions of the plurality of primitives to the particular display element by excluding an EM field contribution of the given primitive to the particular display element.
13. The method of claim 1 , comprising:
obtaining information of a given primitive and an occluder of the given primitive, wherein the given primitive is within the plurality of primitives corresponding to the object;
for each display element of the plurality of display elements, determining a respective part of the given primitive that make no EM field contribution to the display element at an effect of the occluder; and
for each display element of the plurality of display elements, generating a sum of EM field contributions from the plurality of primitives to the display element by excluding an EM field contribution from the respective part of the given primitive to the display element.
14. The method of claim 1 , comprising:
obtaining respective primitive data of each primitive of the plurality of primitives corresponding to the object;
obtaining respective geometric specular information for each primitive of the plurality of primitives;
storing the respective geometric specular information with respective primitive data for each primitive of the plurality of primitives; and
determining a respective EM field contribution of each primitive of the plurality of primitives to each display element of the plurality of display elements by taking into consideration of the respective geometric specular information for the primitive.
15. The method of claim 1 , further comprising:
for each display element of the display, altering a respective control signal with a predetermined calibration value;
applying the altered respective control signal to each display element of the display;
measuring an output of light incident on the display; and
evaluating the predetermined calibration value based on a measurement of the output of the light.
16. The method of claim 1 , further comprising:
for each display element of the display,
obtaining a respective sum of EM field contributions from the plurality of primitives corresponding to the object;
applying a respective mathematical transform to the respective sum of EM field contributions for the display element to obtain a respective transformed sum of EM field contributions for the display element;
determining a respective control signal based on the respective transformed sum of EM filed contributions for the display element; and
modulating a property of the display element based on the determined respective control signal for the display element;
introducing light incident on the display;
measuring an output of the light; and
adjusting one or more coefficients of the respective mathematical transforms of the plurality of display elements based on a result of the measurement of the output of the light.
17. An apparatus comprising:
at least one processor; and
one or more memories coupled to the at least one processor and storing instructions executable by the at least one processor 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 display elements of a display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element based on a predetermined expression for a primitive type that the primitive belongs to, different primitive types corresponding to different predetermined expressions, wherein a primitive represents a geometric or a graphical element for input or output within a computing system and is defined by one or more vertices; 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.
18. A non-transitory machine readable storage medium storing instructions executable by at least one processor 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 display elements of a display by computing, in a three-dimensional (3D) coordinate system, EM field propagation from the primitive to the display element based on a predetermined expression for a primitive type that the primitive belongs to, different primitive types corresponding to different predetermined expressions, wherein a primitive represents a geometric or a graphical element for input or output within a computing system and is defined by one or more vertices; 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.
19. A system comprising:
a display comprising a plurality of display elements; and
a controller coupled to the display and configured to:
for each of a plurality of primitives corresponding to an object, determine 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 based on a predetermined expression for a primitive type that the primitive belongs to, different primitive types corresponding to different predetermined expressions, wherein a primitive represents a geometric or a graphical element for input or output within a computing system and is defined by one or more vertices; 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.
20. The system of claim 19 , further comprising an illuminator arranged adjacent to the display and configured to emit light on the display,
wherein the controller is configured to:
transmit, for each of the plurality of display elements, a respective control signal to the display element, the control signal being for modulating at least one property of the display element based on the sum of the EM field contributions to the display element; and
transmit a timing control signal to the illuminator to activate the illuminator to illuminate the light on the display such that the light is caused by modulated elements of the display to form a volumetric light field corresponding to the object in a 3D space.
21. The system of claim 19 , wherein the controller comprises a plurality of computing units configured to operate in parallel, each of the plurality of computing units being configured to perform respective operations on one or more primitives of the plurality of primitives corresponding to the object.