DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Response to Arguments
This is in response to applicant’s amendment/response filed on 11/10/2025, which has been entered and made of record. Claims 1, 4, 6, 7, 10, and 12 have been amended. Claims 20-21 have been added. Claims 1-22 are pending in the application.
In Remark, page 14, on 103 rejection issue, Applicants argued that ” Zorin neither teaches capsules defined as two spheres joined by a tangent cone, nor any constraint that the intersector solve one quadratic per capsule to obtain the final intersection, nor the tangency-plane-bounded region classification that gates a cone solution versus a single-sphere solution.”
The Examiner respectfully disagrees. The independent claims do not recite calculation of intersectors resulting in solving one quadratic per capsule. The capsule is taught by reference Inigo Quilez (IQ):
In Remark, second paragraph on page 14, on 103 rejection issue, Applicants argued that “Khadiyev does not disclose Applicants' capsule representation-two spheres plus a connecting tangent cone as a single leaf primitive-does not disclose region classification by cone-sphere tangency planes, and does not disclose or suggest the "solve one quadratic to yield the final ray-capsule intersection" constraint. At most, Khadiyev would motivate alternative implicit surfaces for curves (cyclides and frusta), not Applicants' capsule intersector with the claimed single-solve constraint and choose-only-the-nearer-sphere rule outside the between-spheres region.”
The Examiner respectfully disagrees. The independent claims do not recite a calculation and how a selection of the nearest sphere resulting from all 3 ray-intersections and using a single quadratic equation on the nearest sphere. Also, the independent claims do not recite single leaf primitive comprising the capsule. The capsule is taught by reference Inigo Quilez (IQ):
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In Remark, last paragraph on page 14 onto page 15, on 103 rejection issue, Applicants argued that “the cited Shadertoy page is, at best, a demonstration venue for shader snippets that solve standard ray/quadric equations. It does not disclose Applicants' capsule primitive, the tangency-bounded regioning, or the per-capsule single-solve requirement. General examples of quadratic intersection code on Shadertoy add nothing material beyond what is already in the academic references about solving candidate quadratics and selecting the nearest t (again, the opposite of Applicants' structural constraint).”
The Examiner respectfully disagrees. The independent claims do not recite a calculation and how a selection of the nearest sphere resulting from the ray-intersections and resulting in using a single quadratic equation on the nearest sphere. Also, the independent claims do not recite single leaf primitive comprising the capsule not the tangency-bounded regioning.
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In Remark, pages 16-18, on Restriction issue, Applicants requested to rejoin the two groups as they are closely related inventions.
The Examiner respectfully disagrees. The two groups of inventions are
I. Claim 1-12, drawn to a method and a device for rendering curves using ray tracing comprising: performing, for a capsule of the chain of capsules, a closed-form intersection test between the ray and the capsule by solving one quadratic equation to yield a final ray capsule intersection for the respective capsule.
II. Claim 13-20 drawn to a method and a device for rendering curves using ray tracing comprising: determining a smallest distance between the ray and a centerline of the capsule; calculating an offset along the centerline of the capsule; and performing a ray-capsule intersection test based on an intersection between the ray and a blended sphere generated from the offset.
The inventions are distinct, each from the other because of the following reasons:
Inventions I and II are related as combination and subcombination. Inventions in this relationship are distinct if it can be shown that (1) the combination as claimed does not require the particulars of the subcombination as claimed for patentability, and (2) that the subcombination has utility by itself or in other combinations (MPEP § 806.05(c)). In the instant case, the combination as claimed does not require the particulars of the subcombination as claimed because they are separately usable. The subcombination has separate utility such as the invention of group I does not determining a smallest distance between the ray and a centerline of the capsule; calculating an offset along the centerline of the capsule; and performing a ray-capsule intersection test based on an intersection between the ray and a blended sphere generated from the offset; and the invention of group II does not performing, for a capsule of the chain of capsules, a closed-form intersection test between the ray and the capsule by solving one quadratic equation to yield a final ray capsule intersection for the respective capsule.
Applicant’s arguments with respect to independent claims, have been considered but they are not persuasive.
Claim Rejections - 35 USC § 112
The following is a quotation of the first paragraph of 35 U.S.C. 112(a):
(a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention.
The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112:
The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention.
Claims 4-6, 10-12 and 21 are rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention. Claims 4 and 10, each recites “the first region is bounded by planes orthogonal to a centerline of the capsule at respective tangency points between the cone and the first sphere and between the cone and the second sphere, and the second region is outside the bounded segment.” However, the Specification, in par. [0021], only discloses the capsules represent the union of two spheres and a tangent cone connecting the spheres while the Spec. discloses a tangent cone 806 in par. [0077]. The Specification does not disclose the limitations recited in claims 4 and 10.
Claim 21 is rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention. Claim 21 recites
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while the Spec. discloses generic quadratic equation in pars. [0078, 0084].
All dependent claims are also rejected based upon their rejected base claims.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1, 3, 7, and 9 are rejected under 35 U.S.C. 103 as being unpatentable over Khadiyev (US 20190266781) in view of IQ (Capsule - intersection) and Zorin (Ray tracing II).
Regarding claim 1, Khadiyev teaches:
A method for rendering curves using ray tracing, the method comprising:
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tessellating a curve, representing at least a portion of an object in a scene, into a chain of capsules each comprising a first sphere, a second sphere and a cone connecting the first sphere and the second sphere; (Khadiyev at least in Figs. 5-7 and pars. [0019, 0033, 0049, 0053], providing a method of producing a representation of an infinitely smooth curve from a set of geometric primitives, including: generating rays to trace each of the geometric primitives… a chain of Dupin cylide arcs (other geometric primitives: cylinder, cone frustum, capsule…) After the geometric primitives are created by the primitive generator, an “optimizer” can then organize the generated geometric primitives into an optimization structure such as a Bounding Volume Hierarchy (BVH) prior to being ray-traced… Figs. 5 above and [0049], teaches a capsule (cones and spheres) as an example of different types of geometric primitives (or implicit surfaces) that can be generated… and used for ray-tracing to render a representation of infinitely smooth curves.)
generating an acceleration structure comprising the chain of capsules; (Khadiyev at least in Figs. 5-7 and par. [0049, 0053], teaches a chain of Dupin cylide arcs (other geometric primitives: cylinder, cone frustum, capsule…) After the geometric primitives are created by the primitive generator, an “optimizer” can then organize the generated geometric primitives into an optimization structure such as a Bounding Volume Hierarchy (BVH) prior to being ray-traced.)
casting a ray in a space comprising the curve; (Khadiyev at least in Figs. 6-7 and par. [0033], teaches providing a method of producing a representation of an infinitely smooth curve from a set of geometric primitives, including: generating rays to trace each of the geometric primitives.)
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performing, for a respective capsule of the chain of capsules, an intersection test between the ray and the respective capsule; (Khadiyev at least in Figs. 5-7 and pars. [0033, 0049, 0053], teaches determining whether the generated rays intersect respective surfaces of the geometric primitives; a chain of Dupin cylide arcs (other geometric primitives: cylinder, cone frustum, capsule…) After the geometric primitives are created by the primitive generator, an “optimizer” can then organize the generated geometric primitives into an optimization structure such as a Bounding Volume Hierarchy (BVH) prior to being ray-traced.)
rendering the curve based on the intersection test. (Khadiyev [0013])
Khadiyev is silent to teach a closed-form intersection test between the ray and the capsule using a single quadratic equation.
On the other hand, IQ teaches a closed-form intersection test between the ray and the capsule solving one quadratic equation to yield a final ray capsule intersection for the respective capsule (IQ teaches Intersection of a ray and a generic (oriented in any direction) capsule. This computes the intersection with a truncated cylinder and a ONE sphere (as opposed to two). This implies intersection test between the ray and the capsule solving one quadratic equation for a single sphere… at the end yielding a final ray capsule intersection for the respective capsule.) While Zorin in pages 4-11, teaches at least in Cylinder/Cone-ray intersections quadratic equations that picks out the one with min. t… providing a closed-form intersection test for the capsule. The one equation with min. t yields a final ray capsule intersection for the respective capsule as “a final ray capsule intersection" implies one or more ray capsule intersections for different regions of the respective capsule by solving one or more previous/other quadratic equations.
Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art to implement ray intersection testing with a capsule using a quadratic function corresponding to a single sphere from IQ in combine with Zorin for selecting a sphere with a min. t and Khadiyev’s curve-ray intersection testing system. As noticed above, the prior art included each element claimed, although not necessarily in a single prior art reference with the only difference being the lack of actual combination of the elements in a single prior art reference. The examiner finds that one of ordinary skill in the art could combined the elements as claimed by known methods, and that in combination, each element merely performs the same function as it does separately. The combination result would have been predictable.
Regarding claim 3, Khadiyev in view of IQ and Zorin teaches:
The method of claim 1, further comprising:
calculating quadratic coefficients for the closed-form intersection test from input values of the first sphere and the second sphere; and determining whether the ray intersects the cone based on the quadratic coefficients. (Examiner interprets the above limitations as evaluating the quadratic equation having coefficients. The rationale to reject these limitations are in claim 1.)
Claims 7 and 9 recites similar limitations of claims 1 and 3, rationale to reject claims 1 and 3 is applied to claims 7 and 9.
Notes: The combined references, Khadiyev in view of IQ and Zorin, does not recite all the limitations as in claims 4 and 10 and their dependent claims. The combined references does not teach or suggest calculating quadratic coefficients for the single quadratic equation for the closed-form intersection test from input values of the first sphere and the second sphere; and determining whether the ray intersects the cone based on solving the single quadratic equation comprises the calculated quadratic coefficients; wherein the first region is bounded by planes orthogonal to a centerline of the capsule at respective tangency points between the cone and the first sphere and between the cone and the second sphere, and the second region is outside the bounded segment… in viewing its independent claim as a whole.
Allowable Subject Matter
Claim 22 is objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims.
The following is a statement of reasons for the indication of allowable subject matter:
The combined references, Khadiyev in view of IQ and Zorin, does not recite all the limitations as in claim. The combined references does not teach or suggest the memory stores, for each capsule, endpoints of a capsule centerline, radii of the first and second spheres, and a precomputed inverse length of the centerline, and the one or more processors are collectively configured to compute quadratic coefficients using the precomputed inverse length without normalizing the centerline at runtime.
Conclusion
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/PHUC N DOAN/ Examiner, Art Unit 2618