公开(公告)号：US08952977B2

公开(公告)日：2015-02-10

申请号：US12161826

申请日：2007-02-14

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06T15/30 ,  G06T17/20 ,  G09G5/00 ,  G06K9/62 ,  G06K9/34 ,  G06F7/499

CPC classification number: G06F7/49989

Abstract: An improved branch-and-bound process of interval arithmetic subdivision in furtherance of computation of rigorous error bounds on integrated digital scene information for two dimensional display is provided. More particularly, a first aspect of the subject process includes pseudo-randomly subdividing an interval domain comprising a set of interval variables in furtherance of ascertaining a characteristic contribution of the interval variables of said set of interval variables to an image space comprising at least a sub-pixel area. A further aspect, either alone or in combination with the first aspect contemplates pseudo-randomly discarding a select partitioning of interval variables of a set of interval variables of a geometric function from a computed solution of an interval arithmetic branch-and-bound process.

Abstract translation: 提供了一种改进的间隔算术细分的分支绑定过程，用于促进用于二维显示的集成数字场景信息的严格误差界限的计算。 更具体地，本主题过程的第一方面包括伪随机细分包括一组间隔变量的间隔域，以便确定所述间隔变量集合的区间变量对包括至少一个子区域的图像空间的特征贡献 像素区域。 单独地或与第一方面组合的另一方面考虑了从间隔算术分支绑定过程的计算解中伪随机丢弃几何函数的一组间隔变量的间隔变量的选择分割。

公开(公告)号：US08849881B2

公开(公告)日：2014-09-30

申请号：US13114672

申请日：2011-05-24

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F7/00 ,  G06F7/499

CPC classification number: G06F7/485 ,  G06F7/49989 ,  G06F2207/483

Abstract: A logic circuit computes various modal interval arithmetic values using a plurality of arithmetic function units. A multiplexer gates the desired arithmetic values to a storage register.

Abstract translation: 逻辑电路使用多个算术功能单元来计算各种模态间隔算术值。 多路复用器将期望的算术值门控到存储寄存器。

公开(公告)号：US20080256155A1

公开(公告)日：2008-10-16

申请号：US12088368

申请日：2006-10-02

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F17/17

CPC classification number: G06F17/17 ,  G06T17/30

Abstract: A computer executable method of processing a representation of a modal interval polynomial is provided. A representation of a modal interval polynomial is generally provided as input, more particularly, a representation comprising a modal interval function variable and an array of modal interval coefficients. Each modal interval linear interpolation of each of the modal interval coefficients of the array are recursively processed until a single modal interval coefficient remains in the array. For each iteration of the recursive processing, a modal interval linear interpolation operation is executed.

Abstract translation: 提供了一种处理模态间隔多项式的表示的计算机可执行方法。 模态间隔多项式的表示通常作为输入提供，更具体地，提供包括模式间隔函数变量和模态间隔系数的阵列的表示。 阵列的每个模态间隔系数的每个模态间隔线性插值被递归处理，直到单个模态间隔系数保留在阵列中。 对于递归处理的每次迭代，执行模态间隔线性内插操作。

公开(公告)号：US08407269B2

公开(公告)日：2013-03-26

申请号：US12063067

申请日：2006-10-02

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F7/38

CPC classification number: G06F17/10 ,  G06T15/50

Abstract: A computer executable method of processing a representation of a modal interval spherical projection is provided. A representation of a vector comprised of modal intervals X, Y, and Z is provided wherein each modal interval of the modal intervals are delimited by first and second marks of a digital scale. An analytical expression of an azimuthal spherical projection is partitioned into terms of a pair of independent functions wherein a function of the pair exhibits a monotonicity over piecewise domains of the function. A modal interval analysis is performed upon the function wherein arguments of said piecewise domains are modal intervals.

Abstract translation: 提供了一种处理模态间隔球面投影表示的计算机可执行方法。 提供由模态间隔X，Y和Z组成的矢量的表示，其中模态间隔的每个模态间隔由数字刻度的第一和第二标记限定。 方位球面投影的解析表达式被划分成一对独立的函数，其中该对的函数在函数的分段域上表现出单调性。 对所述分段域的参数为模态间隔的函数执行模态间隔分析。

公开(公告)号：US08204926B2

公开(公告)日：2012-06-19

申请号：US12088374

申请日：2006-10-02

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F7/483

CPC classification number: G06F7/49989

Abstract: A computer executable method of performing a modal interval operation, and system for performing same is provided. The method includes providing representations of first and second modal interval operands. Each modal interval operand of the operands is delimited by first and second marks of a digital scale, each mark of the marks comprises a bit-pattern. Each bit-pattern of the bit-patterns of the marks of each of the modal interval operands are examined, and conditions of a set of status flags corresponding to each bit-pattern of the bit-patterns of the marks are set. A bit-mask is computed wherein the mask is based upon the set condition of the status flag sets and a presence/absence of an exceptional arithmetic condition, and a presence/absence of an indefinite operand are each represented by a bit of said bits of said bit mask.

Abstract translation: 提供了执行模式间隔操作的计算机可执行方法，以及用于执行模式间隔操作的系统。 该方法包括提供第一和第二模态间隔操作数的表示。 操作数的每个模式间隔操作数由数字刻度的第一和第二标记界定，标记的每个标记都包含位模式。 检查每个模式间隔操作数的标记的位模式的每个位模式，并且设置与标记的位模式的每个位模式相对应的一组状态标志的条件。 计算位掩码，其中掩码基于状态标志集的设置条件和异常算术条件的存在/不存在，并且不确定操作数的存在/不存在每个由所述位的位 说位掩码

公开(公告)号：US20080263335A1

公开(公告)日：2008-10-23

申请号：US12088382

申请日：2006-10-02

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F15/00 ,  G06F9/00

CPC classification number: G06F7/38 ,  G06F7/483 ,  G06F7/49989

Abstract: A modal interval representation having improved computational utility is provided. The modal interval representation generally includes a binary quantifier, and a set theoretical interval for select permutations of marks of a pair of marks of an IEEE standard 754 digital scale. The set theoretical interval includes combinations of real numbers, infinities, signed zeros, and pseudo-numbers, with select permutations of the marks comprising bounded, unbounded, pointwise and indefinite modal intervals.

Abstract translation: 提供了具有改进的计算实用性的模态间隔表示。 模态间隔表示通常包括二进制量词，以及用于IEEE标准754数字量表的一对标记的标记的选择排列的集合理论间隔。 设定的理论间隔包括实数，无穷大，有符号零和伪数的组合，其中包括有界，无界，点和无限模态间隔的标记的选择排列。

公开(公告)号：US20120254275A1

公开(公告)日：2012-10-04

申请号：US13526062

申请日：2012-06-18

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F7/483

CPC classification number: G06F7/49989

Abstract: A computer executable method of performing a modal interval operation, and system for performing same is provided. The method includes providing representations of first and second modal interval operands. Each modal interval operand of the operands is delimited by first and second marks of a digital scale, each mark of the marks comprises a bit-pattern. Each bit-pattern of the bit-patterns of the marks of each of the modal interval operands are examined, and conditions of a set of status flags corresponding to each bit-pattern of the bit-patterns of the marks are set. A bit-mask is computed wherein the mask is based upon the set condition of the status flag sets and a presence/absence of an exceptional arithmetic condition, and a presence/absence of an indefinite operand are each represented by a bit of said bits of said bit mask.

Abstract translation: 提供了执行模式间隔操作的计算机可执行方法，以及用于执行模式间隔操作的系统。 该方法包括提供第一和第二模态间隔操作数的表示。 操作数的每个模式间隔操作数由数字刻度的第一和第二标记界定，标记的每个标记都包含位模式。 检查每个模式间隔操作数的标记的位模式的每个位模式，并且设置与标记的位模式的每个位模式相对应的一组状态标志的条件。 计算位掩码，其中掩码基于状态标志集的设置条件和异常算术条件的存在/不存在，并且不确定操作数的存在/不存在每个由所述位的位 说位掩码

公开(公告)号：US20080256156A1

公开(公告)日：2008-10-16

申请号：US12088374

申请日：2006-10-02

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F17/10

CPC classification number: G06F7/49989

Abstract: A computer executable method of performing a modal interval operation, and system for performing same is provided. The method includes providing representations of first and second modal interval operands. Each modal interval operand of the operands is delimited by first and second marks of a digital scale, each mark of the marks comprises a bit-pattern. Each bit-pattern of the bit-patterns of the marks of each of the modal interval operands are examined, and conditions of a set of status flags corresponding to each bit-pattern of the bit-patterns of the marks are set. A bit-mask is computed wherein the mask is based upon the set condition of the status flag sets and a presence/absence of an exceptional arithmetic condition, and a presence/absence of an indefinite operand are each represented by a bit of said bits of said bit mask.

Abstract translation: 提供了执行模式间隔操作的计算机可执行方法，以及用于执行模式间隔操作的系统。 该方法包括提供第一和第二模态间隔操作数的表示。 操作数的每个模式间隔操作数由数字刻度的第一和第二标记界定，标记的每个标记都包含位模式。 检查每个模式间隔操作数的标记的位模式的每个位模式，并且设置与标记的位模式的每个位模式相对应的一组状态标志的条件。 计算位掩码，其中掩码基于状态标志集的设置条件和异常算术条件的存在/不存在，并且不确定操作数的存在/不存在每个由所述位的位 说位掩码

公开(公告)号：US08633948B2

公开(公告)日：2014-01-21

申请号：US12596093

申请日：2008-04-16

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G09G5/00 ,  G06T15/50 ,  G09G5/02

CPC classification number: G06T15/503 ,  G09G5/14 ,  G09G2340/10

Abstract: A single-pass, order-independent method in support of rendering transparency effects into a computer generated image is provided. A geometric primitive of a scene is rasterized so as to convert the geometric primitive into a set of pixels. For at least each pixel or subpixel, a stipple pattern is selected from a set of unique stipple patterns. The set of unique stipple patterns is characterized by a select opacity value with the stipple pattern delimiting a unique set of pixels in the computer generated image which contributes to a visible surface determination.

Abstract translation: 提供了一种支持将透明效果渲染到计算机生成的图像中的单程，独立的方法。 将场景的几何图元光栅化，以将几何图元转换为一组像素。 对于至少每个像素或子像素，从一组独特的点状图案中选出点状图案。 独特的点状图案的集合的特征在于选择不透明度值，其中点模式在计算机生成的图像中限定了一组唯一的像素，这有助于可见的表面确定。

公开(公告)号：US07949700B2

公开(公告)日：2011-05-24

申请号：US11569262

申请日：2006-04-05

Applicant: Nathan T. Hayes

Inventor： Nathan T. Hayes

IPC: G06F7/38

CPC classification number: G06F7/485 ,  G06F7/49989 ,  G06F2207/483

Abstract: A logic circuit computes various modal interval (MI) arithmetic values using a plurality of arithmetic function units (AFUs), each dedicated to compute a specific MI arithmetic operation. The AFUs receive first and second MI operand values each encoded in first and second operand signals. Each AFU provides a MI result value encoded in a result signal to a multiplexer. The multiplexer receives a selector signal specifying the MI arithmetic operation desired, and provides to a result register, an output signal encoding the MI result value specified by the selector signal. The result register stores the MI result value.

Abstract translation: 逻辑电路使用多个算术功能单元（AFU）来计算各种模态间隔（MI）算术值，每个算术功能单元专用于计算特定的MI算术运算。 AFU接收在第一和第二操作数信号中编码的第一和第二MI操作数值。 每个AFU将结果信号中编码的MI结果值提供给多路复用器。 多路复用器接收指定所需MI算术运算的选择器信号，并向结果寄存器提供编码由选择器信号指定的MI结果值的输出信号。 结果寄存器存储MI结果值。