IMAGINATION TECHNOLOGIES LIMITED

Patent Trials and Appeals Board

Aug 13, 2020

2019002030 (P.T.A.B. Aug. 13, 2020)

UNITED STATES PATENT AND TRADEMARK OFFICE
UNITED STATES DEPARTMENT OF COMMERCE
United States Patent and Trademark Office
Address: COMMISSIONER FOR PATENTS
P.O. Box 1450
Alexandria, Virginia 22313-1450
www.uspto.gov
APPLICATION NO. FILING DATE FIRST NAMED INVENTOR ATTORNEY DOCKET NO. CONFIRMATION NO.
13/673,872 11/09/2012 Simon Fenney 2645-0150US01 1069
125968 7590 08/13/2020
Potomac Law Group PLLC (IMGTEC)
8229 Boone Boulevard Suite 430
Vienna, VA 22182
EXAMINER
NGO, CHUONG D
ART UNIT PAPER NUMBER
2182
NOTIFICATION DATE DELIVERY MODE
08/13/2020 ELECTRONIC
Please find below and/or attached an Office communication concerning this application or proceeding.
The time period for reply, if any, is set in the attached communication.
Notice of the Office communication was sent electronically on above-indicated "Notification Date" to the
following e-mail address(es):
Eofficeaction@appcoll.com
Patents@potomaclaw.com
vdeluca@potomaclaw.com
PTOL-90A (Rev. 04/07)
UNITED STATES PATENT AND TRADEMARK OFFICE
____________

BEFORE THE PATENT TRIAL AND APPEAL BOARD
____________

Ex parte SIMON FENNEY
____________

Appeal 2019-002030
Application 13/673,872
Technology Center 2100
____________

Before JOHN A. JEFFERY, JUSTIN BUSCH, and
GREGG I. ANDERSON, Administrative Patent Judges.

JEFFERY, Administrative Patent Judge.

DECISION ON APPEAL
This application returns to us after another panel of this Board
affirmed the Examiner’s decision to reject then-pending claims 1–12. Ex
parte Fenney, Appeal 2017-002638 (PTAB June 20, 2017). Prosecution
reopened after that decision, and Appellant now appeals under 35 U.S.C.
§ 134(a) from the Examiner’s subsequent decision to reject claims 1–3, 5–
11, 13, and 14. We have jurisdiction under 35 U.S.C. § 6(b).
We AFFIRM.

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STATEMENT OF THE CASE
Appellant’s invention represents mathematical functions to evaluate
an output for the function for an input value. See Abstract. Because storing
polynomial functions in terms of their coefficients in a lookup table requires
a large amount of memory, the invention stores the same polynomial curves
by fewer stored data. Spec. 6–7. To this end, the invention stores values
that represent control points, including spline control points, to represent the
function. Spec. 7–8. Claim 1 is illustrative:
1. A method for producing a representation of a
mathematical function in a non-transitory computer readable
storage medium, the representation being used to evaluate an
output of the mathematical function for an input value,
comprising:

receiving, in a processor, a mathematical function, for
which a representation is to be created;

approximating the mathematical function by a piecewise
polynomial function over a plurality of intervals, wherein the
mathematical function is approximated over each interval by a
corresponding polynomial function of at least quadratic order;

producing, in the processor, a plurality of spline control
points including a single spline control point for each interval
of a plurality of intervals over which the mathematical function
may be evaluated-to represent the piecewise polynomial
function; and

storing said spline control points in said non-transitory
computer readable storage medium, whereby said stored spline
control points are used to evaluate the mathematical function
for a specific input value within an interval of said plurality of
intervals.

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THE REJECTIONS
The Examiner rejected claims 1–3, 5–11, 13, and 14 under 35 U.S.C.
§ 101 as directed to an abstract idea. Ans. 3–4.1
The Examiner rejected claims 7, 10, and 14 under 35 U.S.C. § 102(b)
as anticipated by David M. Lewis, Interleaved Memory Function
Interpolators with Application to an Accurate LNS Arithmetic Unit, 43 IEEE
TRANS. ON COMPUTERS 974 (1994) (“Lewis”). Ans. 4–5.
The Examiner rejected claims 1–3, 8, 9, 11, and 13 under 35 U.S.C.
§ 103 as unpatentable over Lewis. Ans. 5–6.
The Examiner rejected claims 1, 3, 5, and 6 under 35 U.S.C. § 103 as
unpatentable over Kenneth H. Carpenter, An Introduction to Interpolation
and Splines (Nov. 22, 1999, rev. Nov. 20, 1999, Apr. 24, 2002, Apr. 14,
2004) (“Carpenter”). Ans. 6–7.
The Examiner rejected claims 2, 7–11, 13, and 14 under 35 U.S.C.
§ 103 as unpatentable over Carpenter and Lewis. Ans. 7–9.

THE INELIGIBILITY REJECTION
The Examiner determines that the claimed invention is directed to an
abstract idea, namely computing control points for computing coefficients of
a piecewise polynomial function approximating a mathematical function.
See Ans. 3, 9. According to the Examiner, the recited additional elements,
including (1) a processor or circuitry for implementing the calculations
and/or manipulations of numerical values, and (2) memories for storing

1 Throughout this opinion, we refer to (1) the Appeal Brief filed August 20,
2018 (“Appeal Br.”); (2) the Examiner’s Answer mailed November 5, 2018
(“Ans.”); and (3) the Reply Brief filed January 7, 2019 (“Reply Br.”).
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lookup tables, are generic computer components that do not add significantly
more to the abstract idea. Ans. 3–4, 9–10.
Appellant argues that the claims are eligible because, among other
things, they are directed to a specific technical improvement that stores
spline control points defining a polynomial function instead of storing the
function’s polynomial coefficients—an improvement that is said to reduce
(1) the amount of memory required in Central Processing Unit (CPU) and
Graphics Processing Unit (GPU) systems; (2) operational overhead; and (3)
power consumption. Appeal Br. 9–12; Reply Br. 5–7.

ISSUE
Under § 101, has the Examiner erred in rejecting claims 1–3, 5–11,
13, and 14 as directed to ineligible subject matter? This issue turns on
whether the claims are directed to an abstract idea and, if so, whether the
recited elements—considered individually and as an ordered combination—
transform the nature of the claims into a patent-eligible application of that
abstract idea.

PRINCIPLES OF LAW
An invention is patent-eligible if it claims a “new and useful process,
machine, manufacture, or composition of matter.” 35 U.S.C. § 101.
However, the Supreme Court has long interpreted 35 U.S.C. § 101 to include
implicit exceptions: “[l]aws of nature, natural phenomena, and abstract
ideas” are not patentable. See, e.g., Alice Corp. v. CLS Bank Int’l, 573 U.S.
208, 216 (2014).
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In determining whether a claim falls within an excluded category, we
are guided by the Supreme Court’s two-step framework, described in Mayo
and Alice. Alice, 573 U.S. at 217–18 (citing Mayo Collaborative Servs. v.
Prometheus Labs., Inc., 566 U.S. 66, 75–77 (2012)). In accordance with
that framework, we first determine what concept the claim is “directed to.”
See Alice, 573 U.S. at 219 (“On their face, the claims before us are drawn to
the concept of intermediated settlement, i.e., the use of a third party to
mitigate settlement risk.”); see also Bilski v. Kappos, 561 U.S. 593, 611
(2010) (“Claims 1 and 4 in petitioners’ application explain the basic concept
of hedging, or protecting against risk.”).
Concepts determined to be abstract ideas, and thus patent ineligible,
include certain methods of organizing human activity, such as fundamental
economic practices (Alice, 573 U.S. at 219–20; Bilski, 561 U.S. at 611);
mathematical formulas (Parker v. Flook, 437 U.S. 584, 594–95 (1978)); and
mental processes (Gottschalk v. Benson, 409 U.S. 63, 67 (1972)). Concepts
determined to be patent eligible include physical and chemical processes,
such as “molding rubber products” (Diamond v. Diehr, 450 U.S. 175, 191
(1981)); “tanning, dyeing, making water-proof cloth, vulcanizing India
rubber, smelting ores” (id. at 182 n.7 (quoting Corning v. Burden, 56 U.S.
(15 How.) 252, 267–68 (1854))); and manufacturing flour (Benson, 409 U.S.
at 69 (citing Cochrane v. Deener, 94 U.S. 780, 785 (1876))).
In Diehr, the claim at issue recited a mathematical formula, but the
Supreme Court held that “a claim drawn to subject matter otherwise
statutory does not become nonstatutory simply because it uses a
mathematical formula.” Diehr, 450 U.S. at 187; see also id. at 191 (“We
view respondents’ claims as nothing more than a process for molding rubber
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products and not as an attempt to patent a mathematical formula.”). That
said, the Supreme Court also indicated that a claim “seeking patent
protection for that formula in the abstract . . . is not accorded the protection
of our patent laws, and this principle cannot be circumvented by attempting
to limit the use of the formula to a particular technological environment.”
Id. (citing Benson and Flook); see, e.g., id. at 187 (“It is now commonplace
that an application of a law of nature or mathematical formula to a known
structure or process may well be deserving of patent protection.”).
If the claim is “directed to” an abstract idea, we turn to the second
step of the Alice and Mayo framework, where “we must examine the
elements of the claim to determine whether it contains an ‘inventive
concept’ sufficient to ‘transform’ the claimed abstract idea into a patent-
eligible application.” Alice, 573 U.S. at 221 (quotation marks omitted). “A
claim that recites an abstract idea must include ‘additional features’ to
ensure ‘that the [claim] is more than a drafting effort designed to
monopolize the [abstract idea].’” Id. (alterations in original) (quoting Mayo,
566 U.S. at 77). “[M]erely requir[ing] generic computer implementation[]
fail[s] to transform that abstract idea into a patent-eligible invention.” Id.
In January 2019, the United States Patent and Trademark Office
(“USPTO”) published revised guidance on the application of § 101. See
USPTO’s 2019 Revised Patent Subject Matter Eligibility Guidance, 84 Fed.
Reg. 50 (Jan. 7, 2019) (“Guidance”).2 Under that guidance, we first look to
whether the claim recites:

2 See also October 2019 Update: Subject Matter Eligibility,
https://www.uspto.gov/sites/default/files/documents/peg_oct_2019_update.p
df.
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(1) any judicial exceptions, including certain groupings of
abstract ideas (i.e., mathematical concepts, certain methods of
organizing human activity such as a fundamental economic
practice, or mental processes); and
(2) additional elements that integrate the judicial exception into
a practical application (see MANUAL OF PATENT EXAMINING
PROCEDURE (MPEP) §§ 2106.05(a)–(c), (e)–(h) (9th ed. Rev.
08.2017, Jan. 2018)).
Only if a claim (1) recites a judicial exception, and (2) does not integrate that
exception into a practical application, do we then look to whether the claim:
(3) adds a specific limitation beyond the judicial exception that
is not well-understood, routine, and conventional in the field
(see MPEP § 2106.05(d)); or
(4) simply appends well-understood, routine, and conventional
activities previously known to the industry, specified at a high
level of generality, to the judicial exception.
See Guidance, 84 Fed. Reg. at 56.

ANALYSIS
Claims 1–3, 5–9, 13, and 14: Alice/Mayo Step One
Representative independent claim 1 recites:
A method for producing a representation of a
mathematical function in a non-transitory computer readable
storage medium, the representation being used to evaluate an
output of the mathematical function for an input value,
comprising:

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receiving, in a processor, a mathematical function, for
which a representation is to be created;

approximating the mathematical function by a piecewise
polynomial function over a plurality of intervals, wherein the
mathematical function is approximated over each interval by a
corresponding polynomial function of at least quadratic order;

producing, in the processor, a plurality of spline control
points including a single spline control point for each interval
of a plurality of intervals over which the mathematical function
may be evaluated-to represent the piecewise polynomial
function; and

storing said spline control points in said non-transitory
computer readable storage medium, whereby said stored spline
control points are used to evaluate the mathematical function
for a specific input value within an interval of said plurality of
intervals.

As the Specification explains, because storing polynomial functions in
terms of their coefficients in a lookup table requires a large amount of
memory, the invention stores the same polynomial curves by fewer stored
data. Spec. 6–7. To this end, the invention stores values that represent
control points, including spline control points, to represent the function.
Spec. 7–8.
Turning to claim 1, we first note that the claim recites a method and,
therefore, falls within the process category of § 101. But despite falling
within this statutory category, we must still determine whether the claim is
directed to a judicial exception, namely an abstract idea. See Alice, 573 U.S.
at 217. To this end, we must determine whether the claim (1) recites a
judicial exception, and (2) fails to integrate the exception into a practical
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application. See Guidance, 84 Fed. Reg. at 52–55. If both elements are
satisfied, the claim is directed to a judicial exception under the first step of
the Alice/Mayo test. See id.
The Examiner determines that claim 1 is directed to an abstract idea,
namely computing control points for computing coefficients of a piecewise
polynomial function approximating a mathematical function. See Ans. 3, 9.
To determine whether a claim recites an abstract idea, we (1) identify the
claim’s specific limitations that recite an abstract idea, and (2) determine
whether the identified limitations fall within certain subject matter
groupings, namely, (a) mathematical concepts3; (b) certain methods of
organizing human activity4; or (c) mental processes.5
Here, apart from the recited “non-transitory computer readable storage
medium” and “processor,” all of claim 1’s recited limitations fit squarely
within at least one of the above categories of the USPTO’s guidelines.
When read as a whole, the recited limitations are directed to producing and

3 Mathematical concepts include mathematical relationships, mathematical
formulas or equations, and mathematical calculations. See Guidance, 84
Fed. Reg. at 52.
4 Certain methods of organizing human activity include fundamental
economic principles or practices (including hedging, insurance, mitigating
risk); commercial or legal interactions (including agreements in the form of
contracts; legal obligations; advertising, marketing or sales activities or
behaviors; business relations); managing personal behavior or relationships
or interactions between people (including social activities, teaching, and
following rules or instructions). See Guidance, 84 Fed. Reg. at 52.
5 Mental processes are concepts performed in the human mind including an
observation, evaluation, judgment, or opinion. See Guidance, 84 Fed. Reg.
at 52.
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storing spline control points that are used to evaluate a mathematical
function for an input value within an interval of plural intervals.
That is, apart from the recited “non-transitory computer readable
storage medium” and “processor,” the claimed steps not only recite
mathematical concepts because they include mathematical relationships,
mathematical formulas or equations, and mathematical calculations, but also
mental steps because the recited mathematical steps could be done entirely
mentally or using pen and paper. See Guidance, 84 Fed. Reg. at 52.
First, the limitation calling for “receiving . . . a mathematical function,
for which a representation is to be created” can not only be received and
accessed entirely mentally by merely reading that information on a piece of
paper, it can also be received and accessed from another person, such as a
colleague, by communicating with that person either orally or in writing. Cf.
CyberSource Corp. v. Retail Decisions, Inc., 654 F.3d 1366, 1372 (Fed. Cir.
2011) (noting that a person could construct a map of credit card numbers by
merely writing down a list of credit card transactions made from a particular
IP address); Interval Licensing LLC v. AOL, Inc., 896 F.3d 1335, 1344 (Fed.
Cir. 2018) (noting that a nontechnical human activity of passing a note to a
person who is in a meeting or conversation as illustrating the invention’s
focus, namely providing information to a person without interfering with the
person’s primary activity).
The steps calling for (1) “approximating the mathematical function by
a piecewise polynomial function over a plurality of intervals . . . ”; (2)
“producing . . . a plurality of spline control points including a single spline
control point for each interval of a plurality of intervals over which the
mathematical function may be evaluated to represent the piecewise
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polynomial function”; and (3) “storing said spline control points . . . ,
whereby said stored spline control points are used to evaluate the
mathematical function for a specific input value within an interval of a said
plurality of intervals” can not only be done entirely mentally by merely
thinking about these functions or writing them down, but they also involve
mathematical relationships. See, e.g., In re Grams, 888 F.2d 835, 837 n.1
(Fed. Cir. 1989) (“Words used in a claim operating on data to solve a
problem can serve the same purpose as a formula.”); Elec. Power Grp., LLC
v. Alstom S.A., 830 F.3d 1350, 1354 (Fed. Cir. 2016) (noting that analyzing
information by steps people go through in their minds, or by mathematical
algorithms, without more, are essentially mental processes within the
abstract idea category); Digitech Image Tech., LLC v. Electronics for
Imaging, Inc., 758 F.3d 1344, 1351 (Fed. Cir. 2014) (“Without additional
limitations, a process that employs mathematical algorithms to manipulate
existing information to generate additional information is not patent
eligible.”); Benson, 409 U.S. at 63 (holding ineligible claims involving a
mathematical algorithm and directed to converting binary-coded-decimal
(BCD) numerals into pure binary numerals for use with a computer); accord
CyberSource, 654 F.3d at 1375 (“That purely mental processes can be
unpatentable, even when performed by a computer, was precisely the
holding of the Supreme Court in [Benson].”).
Therefore, apart from the recited “non-transitory computer readable
storage medium” and “processor,” the recited limitations fall squarely within
the mental processes and mathematical concepts categories of the USPTO’s
guidelines and, therefore, recite an abstract idea. See Guidance, 84 Fed.
Reg. at 52.
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Notably, the two elements enumerated above are the only recited
elements beyond the abstract idea, but these additional elements, considered
individually and in combination, do not integrate the abstract idea into a
practical application when reading claim 1 as a whole.
First, we are not persuaded that the claimed invention improves a
computer or its components’ functionality or efficiency, or otherwise
changes the way those devices function, at least in the sense contemplated
by the Federal Circuit in Enfish, LLC v. Microsoft Corp., 822 F.3d 1327
(Fed. Cir. 2016) despite Appellant’s contentions to the contrary (Appeal Br.
10; Reply Br. 5). The claimed self-referential table in Enfish was a specific
type of data structure designed to improve the way a computer stores and
retrieves data in memory. Enfish, 822 F.3d at 1339. To the extent Appellant
contends that the claimed invention uses such a data structure to improve a
computer’s functionality or efficiency, or otherwise change the way that
device functions, there is no persuasive evidence on this record to
substantiate such a contention.
Appellant’s reliance on Research Corp. Technologies, Inc. v.
Microsoft Corp., 627 F.3d 859 (Fed. Cir. 2010) (Reply Br. 5) is also
unavailing. There, the court held eligible claims reciting, among other
things, halftoning gray scale images by using a pixel-by-pixel comparison of
the image against a blue noise mask in which the blue noise mask is
comprised of a random non-deterministic, non-white noise single valued
function to produce visually pleasing dot profiles when thresholded at any
level of said gray scale images. In reaching its eligibility conclusion, the
court noted the claimed invention’s incorporated algorithms and formulas
that controlled masks and halftoning. Id. at 869.
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That is not the case here. To the extent that Appellant contends
otherwise (see Reply Br. 10), we disagree.
To the extent that Appellant contends that the claimed invention is
rooted in technology because it is ostensibly directed to a technical solution
(see Appeal Br. 11–12), we disagree. Even assuming, without deciding, that
the claimed invention can produce and store spline control points that are
used to evaluate a mathematical function for an input value within an
interval of plural intervals faster or more efficiently than doing so manually,
any speed or efficiency increase comes from the capabilities of the generic
computer components—not the recited process itself. See FairWarning IP,
LLC v. Iatric Systems, Inc., 839 F.3d 1089, 1095 (Fed. Cir. 2016) (citing
Bancorp Services, LLC v. Sun Life Assurance Co. of Can. (U.S.), 687 F.3d
1266, 1278 (Fed. Cir. 2012) (“[T]he fact that the required calculations could
be performed more efficiently via a computer does not materially alter the
patent eligibility of the claimed subject matter.”)); see also Intellectual
Ventures I LLC v. Erie Indemnity Co., 711 F. App’x 1012, 1017 (Fed. Cir.
2017) (“Though the claims purport to accelerate the process of finding errant
files and to reduce error, we have held that speed and accuracy increases
stemming from the ordinary capabilities of a general-purpose computer ‘do[]
not materially alter the patent eligibility of the claimed subject matter.’”).
Like the claims in FairWarning, the focus of claim 1 is not on an
improvement in computer processors as tools, but on certain independently
abstract ideas that use generic computing components as tools. See
FairWarning, 839 F.3d at 1095.
Nor is this invention analogous to that which the court held eligible in
McRO, Inc. v. Bandai Namco Games America, Inc., 837 F.3d 1299 (Fed.
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Cir. 2016). There, the claimed process used a combined order of specific
rules that rendered information in a specific format that was applied to create
a sequence of synchronized, animated characters. McRO, 837 F.3d at 1315.
Notably, the recited process automatically animated characters using
particular information and techniques—an improvement over manual three-
dimensional animation techniques that was not directed to an abstract idea.
Id. at 1316.
But unlike the claimed invention in McRO that improved how the
physical display operated to produce better quality images, the claimed
invention here merely produces and stores spline control points that are used
to evaluate a mathematical function for an input value within an interval of
plural intervals. This generic computer implementation is not only directed
to mental processes and mathematical concepts, but also does not improve a
display mechanism as was the case in McRO. See SAP Am., Inc. v.
InvestPic, LLC, 898 F.3d 1161, 1167 (Fed. Cir. 2018) (distinguishing
McRO).
Furthermore, the recited “receiving . . . a mathematical function, for
which a representation is to be created” is insignificant pre-solution activity
that merely gathers data and, therefore, does not integrate the exception into
a practical application for that additional reason. See Bilski, 545 F.3d at 963
(characterizing data gathering steps as insignificant extra-solution activity);
see also CyberSource, 654 F.3d at 1371–72 (noting that even if some
physical steps are required to obtain information from a database (e.g.,
entering a query via a keyboard, clicking a mouse), such data-gathering steps
cannot alone confer patentability); accord Guidance, 84 Fed. Reg. at 55
(citing MPEP § 2106.05(g)).
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On this record, then, the claimed invention does not recite additional
elements that (1) improve a computer itself; (2) improve another technology
or technical field; (3) implement the abstract idea in conjunction with a
particular machine or manufacture that is integral to the claim; (4) transform
or reduce a particular article to a different state or thing; or (5) apply or use
the abstract idea in some other meaningful way beyond generally linking the
abstract idea’s use to a particular technological environment, such that the
claim as a whole is more than a drafting effort designed to monopolize the
exception. See Guidance, 84 Fed. Reg. at 55 (citing MPEP §§ 2106.05(a)–
(c), (e)). In short, the claim’s additional elements do not integrate the
abstract idea into a practical application when reading claim 1 as a whole.
In conclusion, although the recited functions may be beneficial by
producing and storing spline control points that are used to evaluate a
mathematical function for an input value within an interval of plural
intervals, a claim for a useful or beneficial abstract idea is still an abstract
idea. See Ariosa Diagnostics, Inc. v. Sequenom, Inc., 788 F.3d 1371, 1379–
80 (Fed. Cir. 2015).
We, therefore, agree with the Examiner that claim 1 is directed to an
abstract idea.

Claims 1–3, 5–9, 13, and 14: Alice/Mayo Step Two
Turning to Alice/Mayo step two, claim 1’s additional recited elements,
namely the recited “non-transitory computer readable storage medium” and
“processor”—considered individually and as an ordered combination—do
not provide an inventive concept that amounts to significantly more than the
abstract idea when reading claim 1 as a whole. See Alice, 573 U.S. at 221;
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see also Guidance, 84 Fed. Reg. at 56. As noted above, the claimed
invention merely uses generic computing components to implement the
recited abstract idea.
To the extent Appellant contends that the recited limitations, including
those detailed above in connection with Alice step one, add significantly
more than the abstract idea to provide an inventive concept under
Alice/Mayo step two (see Appeal Br. 10–12), these limitations are not
additional elements beyond the abstract idea, but rather are directed to the
abstract idea as noted previously. See BSG Tech. LLC v. Buyseasons, Inc.,
899 F.3d 1281, 1290 (Fed. Cir. 2018) (explaining that the Supreme Court in
Alice “only assessed whether the claim limitations other than the invention’s
use of the ineligible concept to which it was directed were well-understood,
routine and conventional”) (emphasis added); see also Guidance, 84 Fed.
Reg. at 56 (instructing that additional recited elements should be evaluated
in Alice/Mayo step two to determine whether they (1) add specific
limitations that are not well-understood, routine, and conventional in the
field, or (2) simply append well-understood, routine, and conventional
activities previously known to the industry (citing MPEP § 2106.05(d)).
Rather, the claimed “non-transitory computer readable storage
medium” and “processor” are additional recited elements whose generic
computing functionality is well-understood, routine, and conventional. See
Mortg. Grader, Inc. v. First Choice Loan Servs. Inc., 811 F.3d 1314, 1324–
25 (Fed. Cir. 2016) (noting that components such an “interface,” “network,”
and “database” are generic computer components that do not satisfy the
inventive concept requirement); accord Spec. 9 (noting that the disclosed
invention can be implemented on general purpose computers); Ans. 9–10
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(determining that the recited generic computer components are additional
elements that do not add significantly more than the abstract idea).
We reach a similar conclusion regarding the recited insignificant
extra-solution activity, namely “receiving, in a processor, a mathematical
function, for which a representation is to be created” as claimed. That a
mathematical function is received does not mean that this data gathering
function is performed in an unconventional way to add significantly more
than the abstract idea to provide an inventive concept under Alice/Mayo step
two. See Guidance, 84 Fed. Reg. at 56. Given this limitation’s high level of
generality, the recited extra-solution activity does not add significantly more
than the abstract idea to provide an inventive concept under Alice/Mayo step
two. To the extent Appellant contends otherwise (see Appeal Br. 9–12;
Reply Br. 5–7), we disagree.
In conclusion, the additional recited elements—considered
individually and as an ordered combination—do not add significantly more
than the abstract idea to provide an inventive concept under Alice/Mayo step
two. See Alice, 573 U.S. at 221; see also Guidance, 84 Fed. Reg. at 56.
Therefore, we are not persuaded that the Examiner erred in rejecting
claim 1 and claims 2, 3, 5–9, 13, and 14 not argued separately with
particularity.

Claims 10 and 11: Alice/Mayo Step One
The Examiner finds that claim 10 is directed to an abstract idea,
namely computing coefficients of the piecewise polynomial function
approximating using the control points and evaluating the piecewise
polynomial function at a point to obtain an approximating value of the
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mathematical function at that point. Ans. 3, 9. According to the Examiner,
the recited additional elements, including (1) a processor or circuitry for
implementing the calculations and/or manipulations of numerical values, and
(2) memories for storing lookup tables, are generic computer components
that do not add significantly more to the abstract idea. Ans. 3–4, 9–10.
Appellant argues that the claims are eligible because, among other
things, they are directed to a concrete process where memory storage
requirements of a processor that is used to evaluate mathematical functions
is reduced. Appeal Br. 12–13.

ANALYSIS
Claims 10 and 11: Alice/Mayo Step One
Representative independent claim 10 recites:

10. A machine implemented method for evaluating a
mathematical function at a specified value, comprising:

receiving, by a machine, a value for a variable of a
mathematical function to be evaluated;

accessing, from a non-transitory machine readable
medium, a plurality of spline control points, each determined
from the mathematical function to be evaluated, wherein the
spline control points are not themselves required to be an output
value of the mathematical function for an input value to the
mathematical function;

producing by said machine from the plurality of accessed
spline control points, coefficients of a polynomial of a pre-
determined and at least quadratic order, wherein the polynomial
approximates the mathematical function on an interval;

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evaluating by said machine the polynomial for the
received value of the variable to produce an output value; and

using the output value in an application of the
mathematical function.

In assessing claim 10’s eligibility, we first note that the claim recites a
method and, therefore, falls within the process category of § 101. But
despite falling within this statutory category, we must still determine
whether the claim is directed to a judicial exception, namely an abstract idea.
See Alice, 573 U.S. at 217. To this end, we must determine whether the
claim (1) recites a judicial exception, and (2) fails to integrate the exception
into a practical application. See Guidance, 84 Fed. Reg. at 52–55. If both
elements are satisfied, the claim is directed to a judicial exception under the
first step of the Alice/Mayo test. See id.
The Examiner determines that claim 10 is directed to an abstract idea,
namely computing coefficients of a piecewise polynomial function
approximated using spline control points, and evaluating the piecewise
polynomial function at a point to obtain an approximating value of the
mathematical function at that point. See Ans. 3, 9. To determine whether a
claim recites an abstract idea, we (1) identify the claim’s specific limitations
that recite an abstract idea, and (2) determine whether the identified
limitations fall within certain subject matter groupings, namely, (a)
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mathematical concepts6; (b) certain methods of organizing human activity7;
or (c) mental processes.8
Here, apart from the recited “machine” and “non-transitory machine
readable medium,” all of claim 10’s recited limitations fit squarely within at
least one of the above categories of the USPTO’s guidelines. When read as
a whole, the recited limitations are directed to evaluating a mathematical
function using spline control points, and using an output value produced
from that evaluation.
That is, apart from the recited “non-transitory machine readable
medium” and “machine,” the recited steps not only recite mathematical
concepts because they include mathematical relationships, mathematical
formulas or equations, and mathematical calculations, but also mental steps
because the recited mathematical steps could be done entirely mentally or
using pen and paper. See Guidance, 84 Fed. Reg. at 52.
First, the limitation calling for “receiving . . . a value for a variable of
a mathematical function to be evaluated” can not only be received and

6 Mathematical concepts include mathematical relationships, mathematical
formulas or equations, and mathematical calculations. See Guidance, 84
Fed. Reg. at 52.
7 Certain methods of organizing human activity include fundamental
economic principles or practices (including hedging, insurance, mitigating
risk); commercial or legal interactions (including agreements in the form of
contracts; legal obligations; advertising, marketing or sales activities or
behaviors; business relations); managing personal behavior or relationships
or interactions between people (including social activities, teaching, and
following rules or instructions). See Guidance, 84 Fed. Reg. at 52.
8 Mental processes are concepts performed in the human mind including an
observation, evaluation, judgment, or opinion. See Guidance, 84 Fed. Reg.
at 52.
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accessed entirely mentally by merely reading that information on a piece of
paper, it can also be received and accessed from another person, such as a
colleague, by communicating with that person either orally or in writing. Cf.
CyberSource, 654 F.3d at 1372 (noting that a person could construct a map
of credit card numbers by merely writing down a list of credit card
transactions made from a particular IP address); Interval Licensing, 896 F.3d
at 1344 (noting that a nontechnical human activity of passing a note to a
person who is in a meeting or conversation as illustrating the invention’s
focus, namely providing information to a person without interfering with the
person’s primary activity).
The steps calling for (1) “accessing . . . a plurality of spline control
points, each determined from the mathematical function to be evaluated,
wherein the spline control points are not themselves required to be an output
value of the mathematical function for an input value to the mathematical
function”; (2) “producing . . . from the plurality of accessed spline control
points, coefficients of a polynomial of a pre-determined and at least
quadratic order, wherein the polynomial approximates the mathematical
function on an interval”; (3) “evaluating . . . the polynomial for the received
value of the variable to produce an output value”; and (4) “using the output
value in an application of the mathematical function” can not only be done
entirely mentally by merely thinking about these functions or writing them
down, but they also involve mathematical relationships. See, e.g., Grams,
888 F.2d at 837 n.1 (“Words used in a claim operating on data to solve a
problem can serve the same purpose as a formula.”); Elec. Power, 830 F.3d
at 1354 (noting that analyzing information by steps people go through in
their minds, or by mathematical algorithms, without more, are essentially
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mental processes within the abstract idea category); Digitech, 758 F.3d at
1351 (“Without additional limitations, a process that employs mathematical
algorithms to manipulate existing information to generate additional
information is not patent eligible.”); Benson, 409 U.S. at 63 (holding
ineligible claims involving a mathematical algorithm and directed to
converting binary-coded-decimal (BCD) numerals into pure binary numerals
for use with a computer); accord CyberSource, 654 F.3d at 1375 (“That
purely mental processes can be unpatentable, even when performed by a
computer, was precisely the holding of the Supreme Court in [Benson].”).
Therefore, apart from the recited “non-transitory machine readable
storage medium” and “machine,” the recited limitations fall squarely within
the mental processes and mathematical concepts categories of the agency’s
guidelines and, therefore, recite an abstract idea. See Guidance, 84 Fed.
Reg. at 52.
Notably, the two elements enumerated above are the only recited
elements beyond the abstract idea, but these additional elements, considered
individually and in combination, do not integrate the abstract idea into a
practical application when reading claim 10 as a whole.
First, we are not persuaded that the claimed invention improves a
computer or its components’ functionality or efficiency, or otherwise
changes the way those devices function, at least in the sense contemplated
by the Federal Circuit in Enfish despite Appellant’s contentions to the
contrary (Appeal Br. 12–13; Reply Br. 5). The claimed self-referential table
in Enfish was a specific type of data structure designed to improve the way a
computer stores and retrieves data in memory. Enfish, 822 F.3d at 1339. To
the extent Appellant contends that the claimed invention uses such a data
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structure to improve a computer’s functionality or efficiency, or otherwise
change the way that device functions, there is no persuasive evidence on this
record to substantiate such a contention.
Appellant’s reliance on Research Corp. Technologies (Reply Br. 5) is
also unavailing. There, the court held eligible claims reciting, among other
things, halftoning gray scale images by using a pixel-by-pixel comparison of
the image against a blue noise mask in which the blue noise mask is
comprised of a random non-deterministic, non-white noise single valued
function to produce visually pleasing dot profiles when thresholded at any
level of said gray scale images. In reaching its eligibility conclusion, the
court noted the claimed invention’s incorporated algorithms and formulas
that controlled masks and halftoning. Research Corp., 627 F.3d at 869.
That is not the case here. To the extent that Appellant contends
otherwise (see Appeal Br. 10), we disagree.
To the extent that Appellant contends that the claimed invention is
rooted in technology because it is ostensibly directed to a technical solution
(see Appeal Br. 12–13), we disagree. Even assuming, without deciding, that
the claimed invention can evaluate a mathematical function using spline
control points, and use an output value produced from that evaluation faster
or more efficiently than doing so manually, any speed or efficiency increase
comes from the capabilities of the generic computer components—not the
recited process itself. See FairWarning IP, 839 F.3d at 1095 (citing
Bancorp Servs., LLC, 687 F.3d at 1278 (“[T]he fact that the required
calculations could be performed more efficiently via a computer does not
materially alter the patent eligibility of the claimed subject matter.”)); see
also Intellectual Ventures I LLC, 711 F. App’x at 1017 (“Though the claims
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purport to accelerate the process of finding errant files and to reduce error,
we have held that speed and accuracy increases stemming from the ordinary
capabilities of a general-purpose computer ‘do[] not materially alter the
patent eligibility of the claimed subject matter.’”). Like the claims in
FairWarning, the focus of claim 10 is not on an improvement in computer
processors as tools, but on certain independently abstract ideas that use
generic computing components as tools. See FairWarning, 839 F.3d at
1095.
Nor is this invention analogous to that which the court held eligible in
McRO. There, the claimed process used a combined order of specific rules
that rendered information in a specific format that was applied to create a
sequence of synchronized, animated characters. McRO, 837 F.3d at 1315.
Notably, the recited process automatically animated characters using
particular information and techniques—an improvement over manual three-
dimensional animation techniques that was not directed to an abstract idea.
Id. at 1316.
But unlike the claimed invention in McRO that improved how the
physical display operated to produce better quality images, the claimed
invention here merely evaluates a mathematical function using spline control
points, and using an output value produced from that evaluation. This
generic computer implementation is not only directed to mental processes
and mathematical concepts, but also does not improve a display mechanism
as was the case in McRO. See SAP, 898 F.3d at 1167 (distinguishing
McRO).
Furthermore, the recited “receiving . . . a value for a variable of a
mathematical function to be evaluated” is insignificant pre-solution activity
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that merely gathers data and, therefore, does not integrate the exception into
a practical application for that additional reason. See Bilski, 545 F.3d at 963
(characterizing data gathering steps as insignificant extra-solution activity);
see also CyberSource, 654 F.3d at 1371–72 (noting that even if some
physical steps are required to obtain information from a database (e.g.,
entering a query via a keyboard, clicking a mouse), such data-gathering steps
cannot alone confer patentability); accord Guidance, 84 Fed. Reg. at 55
(citing MPEP § 2106.05(g)).
On this record, then, the claimed invention does not recite additional
elements that (1) improve a computer itself; (2) improve another technology
or technical field; (3) implement the abstract idea in conjunction with a
particular machine or manufacture that is integral to the claim; (4) transform
or reduce a particular article to a different state or thing; or (5) apply or use
the abstract idea in some other meaningful way beyond generally linking the
abstract idea’s use to a particular technological environment, such that the
claim as a whole is more than a drafting effort designed to monopolize the
exception. See Guidance, 84 Fed. Reg. at 55 (citing MPEP §§ 2106.05(a)–
(c), (e)). In short, the claim’s additional elements do not integrate the
abstract idea into a practical application when reading claim 10 as a whole.
In conclusion, although the recited functions may be beneficial by
evaluating a mathematical function using spline control points, and using an
output value produced from that evaluation, a claim for a useful or beneficial
abstract idea is still an abstract idea. See Ariosa, 788 F.3d at 1379–80.
We, therefore, agree with the Examiner that claim 10 is directed to an
abstract idea.

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Claims 10 and 11: Alice/Mayo Step Two
Turning to Alice/Mayo step two, claim 10’s additional recited
elements, namely the recited “non-transitory machine readable medium” and
“machine”—considered individually and as an ordered combination—do not
provide an inventive concept that amounts to significantly more than the
abstract idea when reading claim 1 as a whole. See Alice, 573 U.S. at 221;
see also Guidance, 84 Fed. Reg. at 56. As noted above, the claimed
invention merely uses generic computing components to implement the
recited abstract idea.
To the extent Appellant contends that the recited limitations, including
those detailed above in connection with Alice step one, add significantly
more than the abstract idea to provide an inventive concept under
Alice/Mayo step two (see Appeal Br. 12–13), these limitations are not
additional elements beyond the abstract idea, but rather are directed to the
abstract idea as noted previously. See BSG, 899 F.3d at 1290 (explaining
that the Supreme Court in Alice “only assessed whether the claim limitations
other than the invention’s use of the ineligible concept to which it was
directed were well-understood, routine and conventional”) (emphasis
added); see also Guidance, 84 Fed. Reg. at 56 (instructing that additional
recited elements should be evaluated in Alice/Mayo step two to determine
whether they (1) add specific limitations that are not well-understood,
routine, and conventional in the field, or (2) simply append well-understood,
routine, and conventional activities previously known to the industry (citing
MPEP § 2106.05(d)).
Rather, the claimed “non-transitory machine readable medium” and
“machine” are additional recited elements whose generic computing
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functionality is well-understood, routine, and conventional. See Mortg.
Grader, 811 F.3d at 1324–25 (noting that components such an “interface,”
“network,” and “database” are generic computer components that do not
satisfy the inventive concept requirement); accord Spec. 9 (noting that the
disclosed invention can be implemented on general purpose computers);
Ans. 9–10 (determining that the recited generic computer components are
additional elements that do not add significantly more than the abstract
idea).
We reach a similar conclusion regarding the recited insignificant
extra-solution activity, namely “receiving, by a machine, a value for a
variable of a mathematical function to be evaluated” as claimed. That this
value is received does not mean that this data gathering function is
performed in an unconventional way to add significantly more than the
abstract idea to provide an inventive concept under Alice/Mayo step two.
See Guidance, 84 Fed. Reg. at 56. Given this limitation’s high level of
generality, the recited extra-solution activity does not add significantly more
than the abstract idea to provide an inventive concept under Alice/Mayo step
two. To the extent Appellant contends otherwise (see Appeal Br. 9–12;
Reply Br. 5–7), we disagree.
In conclusion, the additional recited elements—considered
individually and as an ordered combination—do not add significantly more
than the abstract idea to provide an inventive concept under Alice/Mayo step
two when reading claim 10 as a whole. See Alice, 573 U.S. at 221; see also
Guidance, 84 Fed. Reg. at 56.
Therefore, we are not persuaded that the Examiner erred in rejecting
claim 10, and claim 11 not argued separately with particularity.
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THE ANTICIPATION REJECTION
Regarding independent claim 7, the Examiner finds that Lewis
discloses every recited element including lookup tables that each store a
respective spline control point determined for a respective interval over
which a mathematical function may be evaluated. Ans. 4–5, 11.
Appellant argues that Lewis does not use spline control points as
claimed. Appeal Br. 7–8. According to Appellant, Lewis’s function values
f(xi) are not spline control points, but rather are actual function values stored
in read-only memory (ROM). Appeal Br. 7–8; Reply Br. 1–3.

ISSUE
Under § 102, has the Examiner erred in rejecting claim 7 by finding
that Lewis discloses lookup tables that store a respective spline control point
determined for a respective interval over which a mathematical function may
be evaluated?

ANALYSIS
We begin by construing the key disputed limitation of claim 7 that
recites, in pertinent part, a spline control point. The Specification does not
define the term explicitly, but does note that smooth surfaces and curves are
frequently modelled using parametric splines, and that spline systems use
“control points” to control the local path of a curve or surface that is a
piecewise polynomial, typically of cubic order. Spec. 5–6. Some spline
systems are interpolating such that the curve actually passes through the
control points. Spec. 6. Other spline systems, however, are approximating
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such that the curve does not generally pass through the control points despite
following their positions. Id.
Although this description informs our understanding of the meaning
of the recited spline control points, it is not so limited. We, therefore,
construe the term “spline control point” with its plain meaning. A special-
purpose dictionary defines the term “spline,” in pertinent part, as follows:
A function used to approximate a specified function on an
interval, consisting of pieces which are defined uniquely on a
set of subintervals, usually as polynomials or some other simple
form, and which match up with each other and the prescribed
function at the end points of the subintervals with a sufficiently
high degree of accuracy.

MCGRAW-HILL DICTIONARY OF SCIENTIFIC & TECHNICAL TERMS 1891 (5th
ed. 1994 Sybil P. Parker ed.) (“McGraw-Hill Dictionary”).
Based on this definition in light of the associated description in the
Specification, a “spline control point” is, therefore, a control point that is
used in connection with a function that approximates a specified function on
an interval, consisting of pieces that are defined uniquely on a set of
subintervals, usually as polynomials or other simple form, and which match
up with each other and the prescribed function at the end points of the
subintervals with a sufficiently high degree of accuracy.
Given this interpretation, we agree with Appellant that the Examiner’s
equating Lewis’s function values f(xi) to the recited spline control points
(see Ans. 4, 11) is problematic on this record. Although Lewis’s system
interpolates polynomial functions, its ROM stores the actual function values
f(xi)—not spline control points that, as noted above, are used in connection
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with a function that approximates a specified function on an interval. See
Lewis 975; Fig. 1.
We reach this conclusion despite the Examiner’s reliance on known
interpolating spline systems where the curve passes through the control
points. Ans. 11 (citing Spec. 6). As noted above, the actual function values
f(xi) stored in Lewis’s ROM are not those that approximate a specified
function on an interval as would be the case with spline control points, but
rather reflect the function itself. See Lewis 975.
Therefore, we are persuaded that the Examiner erred in rejecting (1)
independent claim 7, and (2) dependent claims 10 and 14 for similar reasons.

THE OBVIOUSNESS REJECTION OVER LEWIS
Because Lewis does not teach or suggest producing spline control
points, let alone a single spline control point for each interval of plural
intervals over which a mathematical function may be evaluated as claimed,
we also do not sustain the Examiner’s obviousness rejection of independent
claims 1–3, 8, 9, 11, and 13 for the reasons noted previously.

THE OBVIOUSNESS REJECTION OVER CARPENTER
Regarding independent claim 1, the Examiner finds that Carpenter
produces a representation of a mathematical function, namely x(t), and a
single respective spline control point (Xi) for each interval (i) of plural
intervals over which the mathematical function may be evaluated as claimed.
Ans. 6–7, 11–12. According to the Examiner, Carpenter’s interpolating
polynomials approximate the curve in Equation 1, and that, by drawing a
curve with approximation functions, Carpenter teaches evaluating the
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curve’s mathematical function by approximation functions. Ans. 11.
Although the Examiner acknowledges that Carpenter does not teach
specifically (1) receiving the mathematical function in a processor, and (2)
storing spline control points in a non-transitory computer readable storage
medium, the Examiner nonetheless concludes that these features would have
been obvious to implement the recited method on a computer. Ans. 7–8.
Appellant argues that Carpenter uses control points to generate a
polynomial x(t), and does not produce the control points so that the resulting
polynomial approximates a mathematical function to be evaluated. Appeal
Br. 8; Reply Br. 3–4. According to Appellant, the Examiner improperly
equates both the mathematical function and polynomial that approximates
the mathematical function to the same parameter x(t). Appeal Br. 8; Reply
Br. 3–4.

ISSUE
Under § 103, has the Examiner erred in rejecting claim 1 by finding
that Carpenter would have taught or suggested approximating a received
mathematical function by a piecewise polynomial function over plural
intervals, wherein the mathematical function is approximated over each
interval by a corresponding polynomial function of at least quadratic order
(“the approximation limitation”)?

ANALYSIS
We begin by noting that the disputed approximation limitation of
claim 1 was not before the Board in the earlier appeal. Rather, the
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approximation limitation was added to claim 1 in an amendment filed after
the Board’s Decision. See Amdt filed Dec. 12, 2017.
In the earlier appeal, the Board focused principally on Carpenter’s
teachings in connection with another limitation of then-pending claim 1,
namely producing, for each interval of plural intervals, a single next end
point, or “spline control point,” where the points of each interval define a
polynomial x(t) of third order. Bd. Dec. 13–14. Thus, the question of
whether Carpenter teaches or suggests the approximation limitation was not
before the earlier Board panel.
On this record, we find the Examiner’s rejection problematic
essentially for the reasons indicated by Appellant. Appeal Br. 8; Reply Br.
3–4.
The term “approximation” is defined, in pertinent part, as “[a] result
that is not exact but is near enough to the correct result for some specified
purpose.” McGraw-Hill Dictionary 118.
In Section 1.1, Carpenter notes that a curve’s x, y, and z coordinates
are drawn using three parametric functions: x=x(t); y=y(t); and z=z(t). For
cubic spline interpolation, x(t) is determined using Equation 8 in Carpenter’s
section 2.3.
Given this mathematical identity, we agree with Appellant (Reply Br.
4) that there is simply no approximation of the mathematical function x(t) as
claimed, despite the Examiner’s findings to the contrary. Rather,
Carpenter’s Equation (8) is the mathematical function—not its
approximation as the term is understood in the art, namely a result that is not
exact, but is near enough to the correct result for some specified purpose.
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To be sure, the earlier panel held that Carpenter teaches producing
spline control points (see Bd. Dec. 13–14), and page 6 of Appellant’s
Specification notes that some splines are approximating. Nevertheless, to
the extent that the Examiner finds Carpenter’s spline control point
generation also inherently approximates the recited mathematical function
by a piecewise polynomial function as claimed, the Examiner has not
articulated such a finding, nor will we speculate in that regard here in the
first instance on appeal.
Therefore, on the record before us, we are persuaded that the
Examiner erred in rejecting (1) independent claim 1, and (2) dependent
claims 3, 5, and 6 for similar reasons.

THE OBVIOUSNESS REJECTION OVER CARPENTER AND LEWIS
We also do not sustain the Examiner’s rejection of independent claim
7 that recites, in pertinent part, deriving a polynomial from obtained spline
control points to approximate the mathematical functions over the interval
containing the point at which the mathematical function is to be evaluated.
For reasons similar to those indicated previously, Carpenter fails to teach or
suggest this approximation limitation, and Lewis does not cure that
deficiency.
Therefore, we are persuaded that the Examiner erred in rejecting (1)
independent claim 7; (2) independent claim 10 that recites commensurate
limitations; and (3) dependent claims 8, 9, 11, and 14 for similar reasons.
Because this issue is dispositive regarding our reversing the Examiner’s
rejection of these claims, we need not address Appellant’s other associated
arguments.
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CONCLUSION
In summary:
Claims
Rejected
35 U.S.C.
§
Reference(s)/Basis Affirmed Reversed
1–3, 5–11,
13, 14
101 Eligibility 1–3, 5–11,
13, 14

7, 10, 14 102(b) Lewis 7, 10, 14
1–3, 8, 9, 11,
13
103 Lewis 1–3, 8, 9,
11, 13
1, 3, 5, 6 103 Carpenter 1, 3, 5, 6
2, 7–11, 13,
14
103 Carpenter, Lewis 2, 7–11,
13, 14
Overall
Outcome
1–3, 5–11,
13, 14

TIME PERIOD FOR RESPONSE
No time period for taking any subsequent action in connection with
this appeal may be extended under 37 C.F.R. § 1.136(a)(1).

AFFIRMED