WO2004102339A2 - Removal of acute angles in a design layout - Google Patents

Abstract

Some embodiments of the invention provide novel methods for removing acute angles from routes in a design layout (Figure 34). The method selects a route with several segments. It then identifies an acute angle between first and second contiguous segments of the route (Figure 33). The method next inserts a third segment between the first and second segments, where the third segment has an associated shape that fills the acute angle between the first and second segments (Figure 13).

Description

REMOVAL OF ACUTE ANGLES IN A DESIGN LAYOUT

FIELD OF THE INVENTION

The invention is directed towards removal of acute angles in a design layout.

BACKGROUND OF THE INVENTION

Design engineers design IC's by transforming circuit description of the IC's into

geometric descriptions, called layouts. To create layouts, design engineers typically use

electronic design automation ("EDA") applications. These applications provide sets of

computer-based tools for creating, editing, and analyzing IC design layouts. EDA applications

create layouts by using geometric shapes that represent different materials and devices on

IC's. For instance, EDA tools commonly represent IC components as rectangular objects.

They also use rectangles to represent horizontal and vertical interconnections between

rectangular IC components. The horizontal and vertical interconnects are referred to as

Manhattan interconnects or wiring.

EDA tools typically represent a rectangular object in terms of x and y coordinates of

two opposing vertices of the object (i.e., in terms of x_L0, y o_> and x_H y_Hι). These tools often

represent a non-rectangular object in terms of the x- and y-coordinates of the object's vertices.

Such an approach works well when most of the shapes in the layout are rectangular.

However, certain EDA tools have recently been proposed that support non-

Manhattan wiring. These tools often utilize a large number of non-rectangular shapes. The

traditional approach of specifying a shape in terms of the coordinates of two or more of its

vertices is not efficient for these newer EDA tools. Therefore, there is a need for a novel way

of specifying items in a design layout that has non-rectangular shapes. There is also a need for an efficient way of representing routes with non-Manhattan

edges. One prior technique for representing a Manhattan route specifies the route in terms of

a set of segments and one or more styles. Each segment is a straight line that connects two

points in the design layout. In some cases, the segments of a route are run-length encoded.

This encoding specifies a direction and a length for each segment. In such prior encoding, a

segment's direction can be along 0°, 90°, 180°, and 270°. This encoding also specifies an order

for the segments of the route.

Each segment's style specifies four values that can be used to transform a line-

representation of the segment into a rectangular shape that is a more complete geometric

representation of the segment. These four values include two low delta values, dx_Lo and dy_L0,

and two high delta values, dx_Hι and dy_Hι- The low delta values are subtracted from the

segment's lowest x- and y- values x_Lo, Y_LO to obtain the low x- and y- values (x_{ReC O>} Y_RecLo) of

rectangle that represents the segment, while the high delta values are added to the segment's

highest x- and y-values Xj-π, ym to obtain the high x- and y-values (x_Re__Hi_> Y_RecHi) of the

rectangle. Figure 1 illustrates an example of constructing the rectangle for a segment from the

coordinates and style values of the segment. This prior technique, however, does not support

non-Manhattan routes. Accordingly, there is a need for an efficient representation of routes

that can have non-Manhattan edges.

SUMMARY OF THE INVENTION

Some embodiments of the invention provide novel methods for removing acute angles

from routes in a design layout. The method selects a route with several segments. It then

identifies an acute angle between first and second contiguous segments of the route. The

method next inserts a third segment between the first and second segments, where the third

segment has an associated shape that fills the acute angle between the first and second

segments.

BRIEF DESCRIPTION OF THE DRA INGS

The novel features of the invention are set forth in the appended claims. However, for

purpose of explanation, several embodiments of the invention are set forth in the following

figures.

Figure 1 illustrates an example of constructing the rectangle for a segment from the

coordinates and style values of the segment.

Figure 2 illustrates an octangle data structure used in some embodiments of the

invention.

Figure 3 illustrates two coordinates systems used to define the parameters of the

octangle data structure.

Figure 4 illustrates a -45° diagonal line that can be represented by an equation that is

defined by reference to one of the coordinate systems illustrated in Figure 3.

Figures 5-12 illustrate eight half planes that are defined by the eight parameters of the

octangle data structure illustrated in Figure 2.

Figure 13 illustrates examples of the types of shapes that the octangle data structure

of Figure 2 can represent.

Figures 14-22 illustrate how the shapes illustrated in Figure 13 are represented by

the eight half-plane values.

Figures 23A and 23B illustrate an example that illustrated why some embodiments

define a superfluous half plane of the octangle data structure to abut one of the vertices of the

geometric shape defined by the octangle data structure.

Figure 24 illustrates a process that defines an octangle data structure for a design-

layout item that is initially defined in terms of the x- and y-coordinates of its vertices. Figure 25 illustrates a process that defines an octangle data structure for a design-

layout item that is initially defined in terms of the s- and t-coordinates of its vertices.

Figures 26 and 27 illustrate the use of two different styles for the same segment.

Figure 28 illustrates a process for constructing the polygonal shape of a wire segment

from its direction, length, and associated style information.

Figure 29 illustrates a data structure and database arrangement that is used in some

embodiments in conjunction with the process of Figure 28.

Figure 30 illustrates two different view of a design layout.

Figures 31 and 32 illustrate a process that generates the segment and style

information from a polygon that represents a route segment.

Figure 33 illustrates that an acute 45° angle exists at the juncture between a

horizontal segment and a +45° or -45° segment, and at the junction between a vertical segment

and a +45° or -45° segment.

Figure 34 illustrates a process that is performed for each two contiguous segments SI

and S2 of a route in order to determine whether there is an acute angle between the two

segments, and if so, to remove the acute angle.

Figure 35 illustrates an example for removing an acute angle.

Figure 36 conceptually illustrates a computer system with which some embodiments

of the invention are implemented.

Figures 37-41 illustrate some alternative data structures and coordinate systems that

are used by some embodiments of the invention. DETAILED DESCRIPTION OF THE INVENTION

In the following description, numerous details are set forth for purpose of explanation.

However, one of ordinary skill in the art will realize that the invention may be practiced

without the use of these specific details. In other instances, well-known structures and

devices are shown in block diagram form in order not to obscure the description of the

invention with unnecessary detail.

Some embodiments of the invention provide novel methods for representing items in a

design layout. For instance, some embodiments use a method that represents an item in terms

of n- values that define n-half planes, which when intersected define the shape of the item. In

some embodiments, n is a number greater than four.

Some embodiments use a method that (1) identifies a first set of location data for the

item with respect to a first coordinate system, (2) identifies a second set of location data for

the item with respect to a second coordinate system, and (3) specifies the item in terms of the

first and second set of location data. In some embodiments, both the first and second

coordinate systems have first and second coordinate axes. In some of these embodiments, the

first set of location data are the highest and lowest coordinates of the item on the first and

second coordinate axes of the first coordinate system, while the second set of location data are

the highest and lowest coordinates of the item on the first and second coordinate axes of the

second coordinate system.

Some embodiments use a method that (1) receives a first set of data that defines the

item with respect to a first coordinate system of the design layout, (2) from the first set of

data, generates a second set of data that defines the item with respect to a second coordinate system of the design layout, and (3) specifies the item in terms of both the first and second

sets of data.

In some of the embodiments mentioned above, the first coordinate system is a

Manhattan coordinate system, while the second coordinate system is a non-Manhattan

coordinate system. In other embodiments, the first coordinate system is a non-Manhattan

coordinate system, while the second coordinate system is a Manhattan coordinate system.

I. OCTANGLE DATA STRUCTURE

Some embodiments of the invention provide novel data structures and processes that

efficiently store convex geometric shapes in a design layout, when at least some convex

geometric shapes have at least two sides that are neither parallel nor orthogonal to each other.

In some embodiments, each possible side of the shapes is one of the manufacturing directions.

As used in this document, the term "manufacturing" refers to the process used to manufacture

an IC from its EDA design. Hence, manufacturing directions are the directions available to the

manufacturing process to produce an IC from an EDA design (e.g., to specify the shapes of

cells, pins, interconnects, etc. from the EDA design).

Figures 2-25 illustrate the data structure and processes of some embodiments. The

data structure illustrated in these figures is referred to below as the octangle data structure, as

it is useful for design layouts that have items with horizontal, vertical, and/or ±45° directions.

In the description below, both the wiring and non-wiring geometries of the design layout are

convex shapes, or can be decomposed into convex shapes, that can have horizontal, vertical,

and ±45° sides. One of ordinary skill will realize, however, that some embodiments might use

the octangle data structure in cases where the wiring or non-wiring geometries are more

restricted. For instance, this data structure might be used when the wiring is only in the Manhattan directions or in the ±45° directions, or the non- wiring geometries (e.g., pins and

obstacles) have sides along only in the Manhattan directions or the ±45° directions. The

discussion below focuses on convex polygonal shapes as it assumes that any non-convex

shapes can be broken down into convex polygonal shapes.

As illustrated in Figure 2, the octangle data structure 205 represents each convex

geometric shape in terms of eight values, x_L0, Y _O, S_LO> t_L0, HI, Y_HI> S_HI, and t_m. These eight

values define eight half plane in two coordinate systems. Before describing how 8-half planes

define a convex geometric shape, the two coordinate systems are briefly described. Figure 3

illustrates the two coordinates systems. As shown in this figure, one coordinate system is a

Manhattan coordinate system 305, which is formed by an x-axis 310 and y-axis 315. The

other coordinate system is a 45°-rotated coordinate system 320, which is formed by an s-axis

325 and t-axis 330. The s-axis is at a 45° counterclockwise rotation from the x-axis 310, while

the t-axis is at a 135° counterclockwise rotation from the x-axis 310. In the layouts of some

embodiments, horizontal lines are aligned with the x-axis, vertical lines are aligned with the y-

axis, 45° diagonal lines are aligned with the s-axis, and -45° diagonal lines are aligned with the

t-axis.

In some embodiments, the Manhattan coordinate system is aligned with the

manufacturing grid. Also, some embodiments define the unit length along the s- and t-axes to

be times the unit length along the x- and y-axes, so that the diagonal coordinate system is

L

also aligned with manufacturing grid. In other words, the coordinate resolution along the

diagonal coordinate system 320 is selected such that diagonal lines that traverse through

integer diagonal coordinates can start and terminate on the manufacturing grid, and can intersect, on the manufacturing grid, the Manhattan lines that traverse through integer

Manhattan coordinates. For instance, Figure 4 illustrates a -45° diagonal line 405 that can be

represented by the equation,

s=5.

This line 405 intersects the Manhattan coordinate system at (0, 5) and (5,0). As shown in

Figure 4, 5 units along the s-axis is equivalent to 5 * , or 3.54, units along the Manhattan

2

coordinate system. Given that the unit length along the s- and t-axes is

times the unit

length along the x- and y-axes, the following coordinate-transform equations (A) and (B) can

be used to obtain the s- and t-coordinates of any point from the points x- and y-coordinates.

s = x + y, and (A)

t = y - x. (B)

As mentioned above, the octangle data structure 205 represents each convex geometric

shape in terms of 8 values, where each value defines a half plane that is defined in the design

layout by reference to one of the two coordinate systems 305 and 320. Figure 2 identifies

these 8 values as x_L0, y_Lo_> s_Lo, o, XHI_> YHI, S_HI, and t_ffl. The values XLO, YLO, S_LO, t_L0 are the

smallest coordinates of the shape along the x-, y-, s-, and t-axes (i.e., the smallest x-, y-, s-,

and t-axis values of the shape), while x_ffl, V_HI> s_Hι, and t_Hι are the largest coordinates of the

shape along the x-, y-, s-, and t-axes (i.e., the largest x-, y-, s-, and t-axis values of the shape).

As illustrated in Figures 5-12, the low values (i.e., x_L0, YL_O» ^SL_{O5 L}o) specify a half-plane to

the positive side (i.e., the right or top side) of the value, while the positive values (i.e., m,

y_HI, S_HI, and t_Hι) specify a half-plane to the negative side (i.e., the left or bottom side) of the

value. (Each of these figures illustrates its half plane as a set of dashed lines that terminate on a solid line.) The intersection of these 8 half-planes defines a convex geometric shape.

Specifically, the eight values x_L0, Y_LO, S _O, ^_LO, ^χm, Y_HI, s_ffl, and t_HI define a convex geometric

shape S(x,y) where: fΞSft²

YLO ≤ Y ≤ YHI,

s_L0 ≤ s ≤ S_HI,

LO ^≤ t ≤ t_m,

s = x + y, and

t = y - x.

Figure 13 illustrates examples of the types of shapes that the octangle data structure

205 can represent. As shown in this figure, this data structure can represent a single point, a

line, or any convex polygon that has anywhere from three to eight sides in 8 possible

directions. Figures 14-22 illustrate how the shapes illustrated in Figure 13 are represented

by the 8 half-plane values ₀, YL_O, S_LO, t ₀, XHI, Y_HI, s_m, and t_m. (To simplify these

drawings, Figures 14-22 illustrate each half plane by a dashed line that represents the line on

which the half plane terminates.) The polygonal shapes illustrated in Figures 13-22 can

represent any number of items in the design layout. These items include cells, circuits, circuit

components (such as devices like transistors, capacitors, etc.), obstacles, vias, pins, bounding

polygons, regions of interest, routes, etc. For instance, the polygon in Figure 16 might be all

or a portion of a cell, a circuit, a circuit component, an obstacle, a pin, a via, a bounding

polygon, a region of interest, or a route, etc.

When a convex geometric shape has less than eight sides, one or more of the eight half

planes of the octangle data structure are superfluous (i.e., are not necessary to uniquely identify the boundaries of the shape). For instance, the half plane t_Hι is superfluous in Figure

15, the half planes t_m and s o are superfluous in Figure 16, the half planes t_m, t_Lo, and s_Lo

are superfluous in Figure 17, and so on. When one of the eight half planes is superfluous, it

is canonically defined to abut one of the vertices of the geometric shape. This canonical

definition is part of the above-mentioned definition of the eight half-plane values _LO, YL_O,

SL_O, t_Lo, XHI, YHI, S_HI, and t_ffl. As mentioned above, the values x_L0, y_Lo, s_Lo, t_Lo are defined as

the smallest coordinates of the shape along the x-, y-, s-, and t-axes (i.e., the smallest x-, y-, s-

, and t-axis values of the shape), while x_Hι, YHI, S_HI, and t_Hι are defined as the largest

coordinates of the shape along the x-, y-, s-, and t-axes (i.e., the largest x-, y-, s-, and t-axis

values of the shape).

Some embodiments define a superfluous half plane to abut one of the vertices of the

geometric shape in order to ensure that future calculations that are performed on the shape

provide accurate results. Figures 23A and 23B illustrate an example of this. These figures

present the vertex 2305 of a geometric shape 2310 and a superfluous half plane 2315 that is

defined by the s_Hι parameter. In Figure 23 A, the s_m for the half plane 2315 correctly abuts

the vertex 2305. Hence, as shown in Figure 23 A, an expansion operation that expands the

sides of the geometric shape 2310 by a particular factor, results in a new geometric shape

2320 that correctly has a -45° side (due to the expansion of the half plane 2315) on its upper

right hand corner. Figure 23B, on the other hand, illustrates the s_Hι for the half plane 2315 to

be incorrectly positioned away from the vertex 2305. Consequently, an expansion operation

on this representation incorrectly results in a new geometric shape 2325 that still has a 90°

juncture at the upper left corner of the new geometric shape 2325. Expansion operations are

further described in U.S. Patent Application entitled "Method and Apparatus for Representing Items in a Design Layout" filed 5/21/03, having serial number 10/443,595, and

having a docket number CDN.P0062. This non-provisional application is incorporated herein

by reference and is referred to below in several instances as the "above-incorporated non-

provisional application."

Another advantage of defining a superfluous half plane to abut one of the vertices of

the geometric shape is that this definition simplifies the identification of bounding polygons

and the computation of their widths. As further described in the above-incorporated non-

provisional patent application, the octangle data structure allows EDA tools to quickly

identify the octilinear bounding polygon for a set of items in the design layout. From the

octilinear bounding polygon, the rectilinear Manhattan bounding box can be quickly identified

by simply taking the low and high x and y-values x_L0, Y_LO, X_HI, Y_HI of the octilinear bounding

polygon. Similarly, the 45°-rotated bounding box can be quickly identified by simply taking

the low and high s- and t-values s_Lo, t_Lo S_HI, and t_m of the octilinear bounding polygon. Also,

the width of each of these bounding polygons in a particular direction can be quickly

computed by subtracting the box's low value from the box's high value in the particular

direction.

The octangle data structure 205 can be used to define design-layout items that are in

shape of points, lines, or a variety of convex polygons. Examples of such items include cells,

circuits, circuit components (such as devices like transistors, capacitors, etc.), vias, obstacles,

pins, bounding polygons, regions of interest, and routes. When a design-layout item is

represented by a non-convex shape that is decomposable into two or more convex shapes, the

design-layout item is defined by two or more octangle data structures, where each octangle

data structure represents one of the convex shapes that forms the item. Some embodiments use essentially similar processes to create the octangle data

structure for cells, circuits, circuit components, vias, obstacles, pins, bounding polygons, and

regions of interest, but use a slightly more efficient approach for representing routes. In the

description below, the creation of the more general octangle data structure will be first

described below. This description will then be followed by a description of the efficient

representation of routes in some embodiments of the invention.

Figure 24 illustrates a process 2400 that defines an octangle data structure for a

design-layout item that is initially defined in terms of the x- and y-coordinates of its vertices.

The design-layout item can be any item in the layout, such as a cell, a circuit, a circuit

component, a via, an obstacle, a pin, a bounding polygon, a route and a region of interest. In

some cases, the item is defined only in terms of two of its vertices. For instance, in some

cases, the item is a rectangle that is initially defined only in terms of x- and y-coordinates of

two of its opposing comers (i.e., only in terms of X_L0, Y_LO, and X_HI, Y_HI)- Alternatively, the

item might be defined in terms of three or more of its vertices. For example, the item might be

a polygon that is defined in terms of the x- and y-coordinates of each of its vertices.

As shown in Figure 24, the process 2400 initially defines (at 2405) an octangle data

structure 205 for the design-layout item. At 2410 and 2415, the process then identifies the

lowest x- and y-values of the item, and stores these values as the x_Lo and y_Lo values in the

octangle data structure 205. The item's lowest x- and y-values are respectively the smallest x-

coordinate and the smallest y-coordinate of the item's vertices.

At 2420 and 2425, the process then identifies the highest x- and y-values of the item,

and stores these values as the x_HI and y_m values in the octangle data structure 205. The item's highest x- and y-values are respectively the largest x-coordinate and the largest y-coordinate

of the item's vertices.

The process then performs (at 2430) a coordinate-transform operation. From the x-

and y-coordinates of the vertices of the design-layout item, the coordinate-transform

operation (at 2430) produces an s- ant t-coordinates for each vertex of the design-layout item.

The process produces the s- and t-coordinates for a particular vertex from the x- and y-

coordinates of the particular vertex by using the above-described coordinate-transform

equations (A) and (B). Also, when the item was initially defined in terms of the x- and y-

coordinates of only two of its vertices, the process initially identifies (at 2430) the x- and y-

coordinates of the other vertices of the item, and then performs (at 2430) its coordinate-

transform operation.

At 2435 and 2440, the process then identifies the smallest s- and t-values of the

vertices of the item (i.e., the smallest s- and t-values computed at 2430), and stores these

values as the s_L0 and t_L0 values in the octangle data structure 205. At 2445 and 2450, the

process next identifies the largest s- and t-values of the vertices of the item (i.e., the largest s-

and t-values computed at 2430), and stores these values as the SH_I and t_m values in the

octangle data structure 205. After 2450, the process ends.

The process 2400 of Figure 24 can also be used to define an octangle data structure

that represents an octilinear-bounding polygon of a set of design-layout items that are each

defined in terms of the x- and y-coordinates of two or more vertices. When the process 2400

is used in such a manner, the process 2400 in some embodiments (1) identifies the bounding

polygon's x_L0, Y_LO> ^XH_I and y_Hι values by examining (at 2410-2425) the vertices of all the

items in the set of design-layout items, (2) performs (at 2430) coordinate transform operations on all the vertices of all the items in the set, and (3) identifies the bounding

polygon's s_Lo, t_Lo, S_HI and t_Hι values by examining (at 2435-2450) the vertices of all the items

in the set of design-layout items.

Figure 25 illustrates a process 2500 that defines an octangle data structure for a

design-layout item that is initially defined in terms of the s- and t-coordinates of its vertices.

The design-layout item can be any item in the layout, such as a cell, a circuit, a circuit

component, a via, an obstacle, a pin, a bounding polygon, a route, a region of interest, etc. In

some cases, the item is defined only in terms of two of its vertices. For instance, in some

cases, the item is a rotated rectangle that is initially defined only in terms of s- and t-

coordinates of two of its opposing comers (i.e., only in terms of s_Lo, t_Lo, and s_Hι, t_Hι).

Alternatively, the item might be defined in terms of three or more of its vertices. For example,

the item might be a polygon that is defined in terms of the s- and t-coordinates of each of its

vertices.

As shown in Figure 25, the process 2500 initially defines (at 2505) an octangle data

structure 205 for the design-layout item. At 2510 and 2515, the process then identifies the

lowest s- and t-values of the item, and stores these values as the s_Lo and t_L0 values in the

octangle data structure 205. The item's lowest s- and t-values are respectively the smallest s-

coordinate and the smallest t-coordinate of the item's vertices.

At 2520 and 2525, the process then identifies the highest s- and t-values of the item,

and stores these values as the s_Hι and t_Hι values in the octangle data structure 205. The item's

highest s- and t-values are respectively the largest s-coordinate and the largest t-coordinate of

the item's vertices. The process then performs (at 2530) a coordinate-transform operation. From the s-

and t-coordinates of the vertices of the design-layout item, the coordinate-transform operation

(at 2530) produces an x- ant y-coordinates for each vertex of the design-layout item. The

process produces the x- and y-coordinates for a particular vertex from the s- and t-coordinates

of the particular vertex by using the following coordinate-transform equations (C) and (D),

which are derived from the above-described equations (A) and (B).

x = (s-t), and (C)

y = (s+t). (D)

Also, if the item was initially defined in terms of the s- and t-coordinates of only two of its

vertices, the process initially identifies (at 2530) the s- and t-coordinates of the other vertices

of the item, and then performs (at 2530) its coordinate-transform operation.

At 2535 and 2540, the process then identifies the smallest x- and y-values of the

vertices of the item (i.e., the smallest x- and y-values computed at 2530), and stores these

values as the x_L0 and y_L0 values in the octangle data structure 205. At 2545 and 2550, the

process next identifies the largest x- and y-values of the vertices of the item (i.e., the largest x-

and y-values computed at 2530), and stores these values as the XH_I and y_Hι values in the

octangle data structure 205. After 2550, the process ends.

The process 2500 of Figure 25 can be used to define an octangle data structure that

represents an octilinear-bounding polygon of a set of design-layout items that are each defined

in terms of the s- and t-coordinates of two or more vertices. When the process 2500 is used in

such a manner, the process 2500 in some embodiments (1) identifies the polygon's s_Lo, t_Lo,

s_Hι and t_m values by examining (at 2510-2525) the vertices of all the items in the set of

design-layout items, (2) performs (at 2530) coordinate transform operations on all the vertices of all the items in the set, and (3) identifies the polygon's _LO, Y_LO, X_HI and y _Hι values

by examining (at 2535-2550) the vertices of all the items in the set of design-layout items.

It might be necessary to identify the octilinear-bounding polygon of a set of design-

layout items that includes (1) a first sub-set of items that are defined in terms of the x- and y-

coordinates of two or more of their vertices, and (2) a second sub-set of items that are defined

in terms of the s- and t-coordinates of two or more of their vertices. In such a case, some

embodiments perform two sets of coordinate transform operations initially to obtain x-, y-, s-

and t-vertex coordinates for each item in the set. These embodiments then identify the

smallest and largest x-, y-, s- and t-vertex coordinate values in the set and store these values in

an octangle data structure. The initial coordinate-transform operations are not needed when

each item in the set is expressed in terms of x-, y-, s-, and t-coordinates.

In some cases, some embodiments do not perform the process 2400 or the process

2500 to identify the octangle data structure of a design-layout item. Instead, in such cases,

these embodiments define the octangle data structure while defining the design-layout item.

For instance, such is the case when some embodiments define an item based on a user's input.

π. REPRESENTATION OF ROUTES

Some embodiments of the invention define each route in terms of one or more

segments and one style for each segment. Each segment is a straight line that connects two

points in the design layout. Some embodiments run-length encode the segments of a route.

Such an encoding specifies each segment in terms of a direction D and a length L. A segment's

direction can be along any of the 8 available routing directions, which are 0°, 45°, 90°, 135°,

180°, 225°, 270°, and 315°. This encoding also specifies an order for the segments of the

route. Such an order can be specified in a variety of ways, such as a singly or doubly linked list, a numbering scheme, etc. In some embodiments, the segments are stored in a 1-

dimensional array. In these embodiments, the order of the segments is the order that they

appear in the array.

The run-length encoding of a route also typically specifies at least a starting point for

the route. From this starting point, a line representation of the route can be constructed as

follows. The first segment Si is initially constructed as a segment that starts at the starting

point and terminates a distance d away from this starting point in the first segment's direction

Dl. When the first segment is in a horizontal or vertical direction, the distance d equals the

length L of the first segment. On the other hand, when the first segment is in a ±45°

direction, the distance d equals the length W,χ of the first segment times square root of 2 (i.e., d

Each subsequent segment of the route is then constructed by performing an iterative

operation. During each iteration, the operation constructs one segment, referred to as the

current segment So This current segment Sc starts at the termination of the previously

constructed segment S_P, which is before the current segment in the route in the segment order

that is being constructed. The current segment Sc terminates at a point that is a distance d_c

(where d_c is the current segment's length- L_c when the segment is in a horizontal or vertical

direction, or is the current segment's length L_C* V2 when the segment is in a ±45° direction)

away from the previous segment's termination point in the current segment's direction D.

This iterative operation terminates once it has constructed the last segment.

As mentioned above, some embodiments also define a style for each segment of a

route. A style specifies eight values that can be used to transform a line-representation of a

segment into a convex polygonal shape that represents a more complete geometric representation of the segment. These eight values include four low values, dx o, dy_L0, ds_Lo,

dt ₀, and four high values, dx_m, dy_Hι, ds_Hι, and dt_m. The low values are subtracted from the

segment's lowest x-, y-, s- and t-values to obtain the low values of convex polygon that

represents the segment, while the high values are added to the segment's highest x-, y-₃ s-, and

t-values to obtain the high values of the convex polygon.

Figures 26 and 27 illustrate the use of two different styles for the same segment

2600. The segment 2600 connects the x,y coordinates (1,3) and (5,7), which map to the s,t

coordinates (4,2) and (12,2). In the example illustrated in Figure 26, the style is specified by

the following eight values:

dx_L0=2, dy_L0=2, ds_L0=3, dt_L0=3, dx_Hι=2, dy_HI=2, ds_Hr=3, dt_Hr=3.

Figure 26 illustrates that the subtraction of the style's low values from the corresponding

low values of the segment 2600 identifies the following four half-planes:

while the addition of the style's high values from the corresponding high values of the segment

2600 identifies the following four half-planes:

X_HI=7, y_ffl=9, S_HI=15, t_m=5.

As shown in Figure 26, these eight half planes define an octagon 2605.

In the example illustrated in Figure 27, the style is specified by the following eight

values:

dx_L0=2, dy_L0=2, ds_L0=3, dt_L0-=3, dx_m-=2, dy_m=2, ds_ffl=l, dt_Hι=3.

Figure 27 illustrates that the subtraction of the style's low values from the corresponding

low values of the segment 2600 identifies the following four half-planes:

while the addition of the style's high values from the corresponding high values of the segment

2600 identifies the following four half-planes:

XH_I ⁼7, y_Hi⁼ , s_Hι=13, t_m=5.

As shown in Figure 27, these eight half planes define a hexagon 2705. Accordingly, in the

example illustrated in Figures 26 and 27, the use of two different styles for the same segment

2600 resulted in two different convex polygonal shapes 2605 and 2705 for the segment.

Figure 28 illustrates a process for constructing the polygonal shape of a wire segment

from its direction, length, and associated style information. This process works in conjunction

with a data structure and database arrangement illustrated in Figure 29. Figure 29 illustrates

that a segment is represented as a segment data structure 2905 that stores the length and

direction of the segment, and potentially other segment identifying indicia, such as relational

data that specifies the order of the segment in the segment's route. As shown in this figure,

the segment data structure also includes an index 2910 that identifies a record 2920 in a style

table 2915. Each record in the style table 2915 is identifiable by a unique style index 2910.

Also, each record specifies a unique set of 8 delta values, dx_Lo, dy_L0, ds_Lo, dt_L0, dx_Hι, dy_m,

ds_Hι, and dt_m.

As shown in Figure 28, the process 2800 initially identifies (at 2805) the x-, y-, s-,

and t-coordinates of the start and end points of the segment from the segment's start

coordinate, direction, and length. As mentioned above, a particular segment's start coordinate

is the termination coordinate of the previous segment in the route, unless the particular

segment is the first segment, in which case its start coordinate is the start point of the route.

The segment's end point is a point that is a distance d away from the segment's start point in

the segment's direction D. As mentioned above, the distance d is the segment's length L when the segment is in a horizontal or vertical direction, or is the segment's length times square root

of 2 (L* 2 ) when the segment is in a ±45° direction.

The process then retrieves (at 2810) the delta values (dx o, dy_L0, ds_L0, dt_L0, dx_HI,

dym, ds_m, and dt_Hι) associated with the style of the segment. It then computes (at 2815) the

x-low value x_PL0 of the polygon that is to represent the segment by subtracting dx_L0 from the

segment's X _O- The process next computes (at 2820) the y-low value y_PLo of the polygon by

subtracting dy_Lo from the segment's y_Lo It then computes (at 2825) the s-low value s_PLo of

the polygon by subtracting ds_Lo from the segment's s ₀- The process next computes (at

2830) the t-low value t_PLo of the polygon by subtracting dt_L0 from the segment's t_L0-

The process then computes (at 2835) the x-high value X_PHI of the polygon that is to

represent the segment by adding dx_m to the segment's X_HI. The process next computes (at

2840) the y-high value y_PHι of the polygon by adding dy_m to the segment's y_HI. It then

computes (at 2845) the s-high value s_PHι of the polygon by adding ds_m to the segment's s_m.

The process next computes (at 2850) the t-high value trøi of the polygon by adding dt_m to

the segment's t_Hι- The computed parameters x_PL0, y_Pιχ_>, S_PL_O, _PLo, XPHI, YPH_I, ^S _PHI_> and t_PHι for

the polygon define the shape of the polygon. Accordingly, these values can be stored in an

octangle data structure to represent the polygon.

The process 2800 can be used in a variety of different scenarios when it is desirable to

specify the actual geometry of the routes from their segment and style information. For

instance, this process could be used to generate a display of the routes, to output data to a

GDS file, to perform extraction, to estimate routing capacity, etc.

Figure 30 illustrates two different views of a design layout 3000 that includes three

routes 3005, 3010, and 3015. The first view 3020 illustrates each route in terms of a set of line segments that are abutting. The second view 3025 illustrates each route in terms of a set

of polygons that partially overlap. Each of the polygons in the second view corresponds to a

particular segment in the first view. As described above by reference to Figure 28, each

particular polygon in the second view can be generated from its corresponding segment by

applying the delta parameters of the segment's associated style to the style's endpoint values.

Hence, to store efficiently the routes illustrated in Figure 30, some embodiments (1) store

each route in terms of the route's set of segments, and (2) as illustrated in Figure 29, specify

each segment in terms of its length, direction, and style-table index. The style table index of a

segment, in turn, identifies a set of delta parameters, which when applied to the segment's

endpoints specify eight half planes that define the segment's polygonal shape.

Figure 31 illustrates a process 3100 that generates the segment and style information

from a polygon that represents a route segment. An EDA tool performs this process when

the tool does not have the style and segment information. For instance, a power router might

perform such an operation if it does not use a pre-defined style for the routes that it defines.

It should be noted that when an EDA tool has the style and/or segment information

associated with a polygonal representation of a route, the tool simply generates the needed

segment and style information from the eight half planes that represent the polygon and the

available segment and style information.

As shown in Figure 31, the process 3100 initially identifies (at 3105) the coordinate

axis that will be parallel to the segment that the process will define for the polygon that

represents the route segment. Figure 32 illustrates how some embodiments identify this

coordinate axis. This figure illustrates a polygon 3205 for which segment and style data needs

to be generated. For the polygon 3205, some embodiments identify the Manhattan bounding box 3210 and 45°-rotated bounding box 3215 that enclose the polygon. These bounding

polygons can be identified according to the approach described above, which is further

elaborated in the above-incorporated non-provisional patent application.

These embodiments next identify the bounding box with the smallest area, and then

based on the identified bounding box, specify the coordinate axis along which the route

segment will be defined. For instance, when the Manhattan bounding box has the smaller area,

then the process 3100 determines (at 3105) whether the polygon's width is longer along the x-

axis than its width along the y-axis. If so, the process identifies (at 3105) the x-axis as the

coordinate axis. Otherwise, the process identifies (at 3105) the y-axis as the coordinate axis.

On the other hand, when the 45°-rotated bounding box has the smaller area, then the process

determines (at 3105) whether the polygon's width is longer along the s-axis than its width

along the t-axis. If so, the process identifies (at 3105) the s-axis as the coordinate axis.

Otherwise, the process identifies (at 3105) the t-axis as the coordinate axis. In the example

illustrated in Figure 32, the rotated bounding box 3215 has the smaller area and the polygon's

width along the s-axis is larger than its width along the t-axis. Accordingly, the s-axis is

identified (at 3105) as the coordinate axis for the segment that is to be defined for the polygon

3205.

After identifying the coordinate axis at 3105, the process defines (at 3110) the

segment as a line that is parallel to the identified coordinate axis, and that is half way between

the polygon's high and low coordinates on the coordinate axis perpendicular to the identified

axis. At this stage, the process also specifies (at 3110) the x-, y-, s-, and t-coordinate values

of the two endpoints of the segment. These two endpoints are two points on the boundary of

the polygon that are intersected by the defined segment (i.e., are intersected by a line that is parallel to the identified coordinate axis and that is half way between the polygon's high and

low coordinates on the coordinate axis perpendicular to the identified axis). For instance, in

the example illustrated in Figure 32, the segment 3220 is identified to be parallel to the s-axis

and halfway between the high and low t-axis coordinates of the polygon 3205. The endpoints

of the segment 3220 are points 3225 and 3230.

The process then identifies the 8 delta values, dx_L0, dy_L0, ds_L0, dt_LO, dx_m, dy_ffl, ds_m,

and dt-eπ, associated with the style. Specifically, it computes (at 3115) the low delta x- value

dx ₀ by subtracting the polygon's x-low value Xp_Lo from the x-low value _L0 of the segment.

The process then computes (at 3120) the low delta y- value dy_Lo by subtracting the polygon's

y-low value y_P o from the y-low value y_L0 of the segment. It then computes (at 3125) the

low delta s-value ds_LO by subtracting the polygon's s-low value s_PL0 from the s-low value s_L0

of the segment. The process next computes (at 3130) the low delta t-value dt o by

subtracting the polygon's t-low value t_P o from the t-low value t_Lo of the segment.

The process then computes (at 3135) the high delta x-value dx_Hι by subtracting the x-

high value x_m of the segment from the polygon's x-high value x_PHI. It next computes (at 3140)

the high delta y-value dy_m by subtracting the y-high value y_Hι of the segment from the

polygon's y-high value y_Pκι. The process then computes (at 3145) the high delta s-value ds_Hι

by subtracting the s-high value s_m of the segment from the polygon's s-high value s_PHι- It next

computes (at 3150) the high delta t-value dt_Hι by subtracting the t-high value t_Hι of the

segment from the polygon's t-high value t_PHι.

The computed delta values dx_L0, dy_L0, ds_L0, dt_L0, dx_Hι, dy_Hι, dsπi, and dt_m define a

style, which can be stored and indexed in a database table, such as table 2915 of Figure 29.

This style can be indexed by a segment data structure (such as structure 2905 of Figure 29) for the segment specified at 3110. The direction of this segment would be one of the two

directions parallel to the coordinate axis identified at 3105. The length of this segment would

be the distance between the two endpoints of the segment.

HI. ACUTE ANGLE REMOVAL

Some embodiments of the invention provide a method for removing acute angles

between edges of a route. In some of these embodiments, each edge of the route is represented

in terms of a segment and a style as described above. In some embodiments, an acute angle is

an angle that is less than 90°. Accordingly, in these embodiments, two segments of a route

form an acute angle if an angle less than 90° is created at their juncture. In the embodiments

that have routes with horizontal, vertical, and/or ±45° segments, an acute angle is 45°. As

illustrated in Figure 33, such an acute angle exists at the juncture between a horizontal

segment and a +45° or -45° segment, and at the junction between a vertical segment and a

+45° or -45° segment.

Figure 34 illustrates a process 3400 that is performed for each two contiguous

segments SI and S2 of a route in order to determine whether there is an acute angle between

the two segments, and if so, to remove the acute angle. Two segments are contiguous in a

route if the end of one segment is the beginning of the next segment. The process 3400 will be

described below by reference to Figure 35, which illustrates the juncture between two

segments 3505 and 3510.

As shown in Figure 34, the process 3400 initially determines (at 3405) whether an

acute angle is formed between the two segments SI and S2. When routes have segments with

horizontal, vertical, and/or ±45° directions, an acute angle is a 45° angle that is formed at the

juncture between abutting horizontal and diagonal segments and abutting vertical and diagonal segments. Some embodiments store whether there is an acute angle between different

combination of segments in a look-up table. In these embodiments, the process 3400 makes

the determination at 3405 by identifying the directions of the two segments SI and S2 and

then examining the look-up table to determine whether there is an acute angle at the juncture

between SI and S2. In the example illustrated in Figure 35, there is an acute 45° angle

between the segments 3505 and 3510.

If the process 3400 determines (at 3405) that there is no acute angle between SI and

S2, the process terminates. Otherwise, the process specifies a new segment S3 at 3410. The

process then specifies (at 3415) the length of this segment as 0. From a look-up table that

stores an index into the style table 2915 for each combination of adjacent segments, the

process 3400 then retrieves (at 3420) an index into the style database table 2915 for the pair

of segments SI and S2. As further described below, the style identified by the retrieved index

can be used in conjunction with the zero-length segment S3 to specify a polygon that fills the

acute angle formed by the particular pair of segments SI and S2. At 3420, the process

associates the retrieved style-table index with the zero-length segment specified at 3410.

After 3420, the process then inserts (at 3425) the zero-length segment S3 between

segments SI and S2 on the ordered set of segments of the route. How this insertion is done

depends on the manner that the ordered set of segments are specified. For instance, if the

ordered set of segments are established in terms of a linked list, a segment can be inserted by

disconnecting one single or double link, and establishing links between the zero-length

segment and the two previously connected segments. On the other hand, when the segments

are ordered in a 1 -dimensional array, a segment can be inserted through an insertion function

that (1) pushes all the segments after the insertion location of the zero-length segment down by one and then (2) stores the zero-length segment in the insertion location. When no such

function exists, the segment can be inserted in the array by reading out the segments from the

array, inserting the segment at the right location in the order, and then re-storing the segments

in the array.

In the example illustrated in Figure 35, the process 3400 would retrieve (at 3420) a

style-table index that is stored in the look-up table for the combination of a 0° segment and a

135° segment, or a -45° segment and a 180 segment. The retrieved style table index would

specify the following eight delta values:

dx_LO=20, dy_L0-=-5, ds_LO=20, dt_LO=-10, dx_m=-10, dy_Hι=20, ds_Hι=-5, dt_m=25.

In Figure 35, the zero-length segment S3 that is inserted between segments 3505 and 3510 is

represented as a node 3515. As shown in Figure 35, the eight delta values of the style

identified by the retrieved style index (i.e., the retrieved dx ₀, dy_L0, ds_L0, dt_L0, dx_Hι, dy_m,

ds_Hι, dt_Hι), specify a triangle 3520 that fills the acute angle created at the juncture of the

segments 3505 and 3510.

IV. COMPUTER SYSTEM

Figure 36 conceptually illustrates a computer system with which some embodiments

of the invention are implemented. Computer system 3600 includes a bus 3605, a processor

3610, a system memory 3615, a read-only memory 3620, a permanent storage device 3625,

input devices 3630, and output devices 3635.

The bus 3605 collectively represents all system, peripheral, and chipset buses that

communicatively connect the numerous internal devices of the computer system 3600. For

instance, the bus 3605 communicatively connects the processor 3610 with the read-only

memory 3620, the system memory 3615, and the permanent storage device 3625. From these various memory units, the processor 3610 retrieves instructions to execute

and data to process in order to execute the processes of the invention. The read-only-memory

(ROM) 3620 stores static data and instructions that are needed by the processor 3610 and

other modules of the computer system. The permanent storage device 3625, on the other

hand, is read-and-write memory device. This device is a non-volatile memory unit that stores

instruction and data even when the computer system 3600 is off. Some embodiments of the

invention use a mass-storage device (such as a magnetic or optical disk and its corresponding

disk drive) as the permanent storage device 3625. Other embodiments use a removable storage

device (such as a floppy disk or zip® disk, and its corresponding disk drive) as the

permanent storage device. Like the permanent storage device 3625, the system memory 3615

is a read-and-write memory device. However, unlike storage device 3625, the system memory

is a volatile read-and-write memory, such as a random access memory. The system memory

stores some of the instructions and data that the processor needs at runtime. In some

embodiments, the invention's processes are stored in the system memory 3615, the

permanent storage device 3625, and/or the read-only memory 3620.

The bus 3605 also connects to the input and output devices 3630 and 3635. The input

devices enable the user to communicate information and select commands to the computer

system. The input devices 3630 include alphanumeric keyboards and cursor-controllers. The

output devices 3635 display images generated by the computer system. For instance, these

devices display IC design layouts. The output devices include printers and display devices,

such as cathode ray tubes (CRT) or liquid crystal displays (LCD).

Finally, as shown in Figure 36, bus 3605 also couples computer 3600 to a

network 3665 through a network adapter (not shown). In this manner, the computer can be a part of a network of computers (such as a local area network ("LAN"), a wide area network

("WAN"), or an Intranet) or a network of networks (such as the Internet). Any or all of the

components of computer system 3600 may be used in conjunction with the invention.

However, one of ordinary skill in the art would appreciate that any other system

configuration may also be used in conjunction with the present invention.

While the invention has been described with reference to numerous specific details,

one of ordinary skill in the art will recognize that the invention can be embodied in other

specific forms without departing from the spirit of the invention. For instance, some

embodiments might also include a layer attribute in the octangle data structure 205 of Figure

2, while other embodiments might specify the layer information in some other manner.

Also, several of the above-described embodiments use the octangle data structure 205,

which is useful to represent design-layout items with horizontal, vertical, and ±45° directions.

Other embodiments, however, might use other types of data structures that are optimized for

other types of design-layout items.

For example, some embodiments define routes according to a hexagonal wiring model

that specifies three routing directions that are offset from each other by 60°. For such a wiring

model, some embodiments use a hexangle data structure 3700 that is illustrated in Figure 37.

This data structure stores eight values that are defined with respect to a hexagonal coordinate

system 3800 illustrated in Figure 38. As shown in Figure 38, the hexagonal coordinate

system includes a Manhattan coordinate system and a rotated coordinate system. The rotated

coordinate system includes u- and v-axes. The u-axis is at a 60° clockwise rotation from the

y-axis, while the v-axis is at a 60° counterclockwise rotation from the y-axis. The hexangle

data structure represents each convex geometric shape in terms of eight values, XL₀, Y _O, U _O, V _O, ^X _HI, ym, u ι, and V_HI- These eight values define eight half planes that bound a design-

layout item in the Manhattan and rotated coordinate systems. The eight values are useful in

representing design-layout items (such as pins) that have sides in the Manhattan and ±30°

directions (where 30° is defined with respect to the Manhattan coordinate system). In

addition, the y-, u-, and v-values are useful in representing routes that have segments parallel

to the y-, u-, and v-axis.

In some cases, the hexagonal wiring model specifies the x-axis as one of the routing

directions. In these cases, the three routing directions are 0°, 60°, and -60°. In these cases, the

u- and v-values of the hexangle data structure 3700 would be defined by reference to the

coordinate system of Figure 39. This coordinate system is similar to the coordinate system

3800 of Figure 38, except that the u'- and v'-axes in Figure 39 are rotated by 60° with

respect to the x-axis.

Alternatively, instead of specifying a data structure that is optimized for one of the

two potential hexagonal wiring models mentioned above, some embodiments use a symmetric-

hexangle data structure 4000 illustrated in Figure 40. This data structure is defined for the

coordinate system of Figure 41, which includes a Manhattan coordinate system, a 30°-

rotated coordinate system, and a 60°-rotated coordinate system. The 30°-rotated coordinate

system includes two axes, u- and v-axes, that are rotated by 30° with respect to the x-axis

(i.e., are rotated by 60° with respect to the y-axis). The 60°-rotated coordinate system

includes two axes, u'- and v'-axes, that are rotated by 60° with respect to the x-axis.

The symmetrical hexangle data structure 4000 represents each convex geometric shape

in terms of twelve values, x_L0, y_Lo, u_Lo, v_Lo, U'LO, V'LO, XHI, YHI, u_m, v_Hι, '_Hι, and v'_m. These

twelve values define twelve half planes that bound a design-layout item in the three sub- coordinate systems of the coordinate system of Figure 41. The twelve values are useful in

representing design-layout items (such as pins or routes) that might have sides in the

Manhattan, ±30°, and ±60° directions. Thus, one of ordinary skill in the art would

understand that the invention is not to be limited by the foregoing illustrative details, but

rather is to be defined by the appended claims.

Claims

CLAIMSWe claim:

1. A method of removing acute angles from routes in a design layout, the method

comprising:

a) selecting a route with a plurality of segments;

b) identifying an acute angle between first and second contiguous

segments of the route;

c) inserting a third segment between the first and second segments,

wherein the third segment has an associated shape that fills the acute angle between the first

and second segments.

2. The method of claim 1 , wherein each segment has a length and the length of the

third segment is zero.

3. The method of claim 2, wherein each segment has an associated shape, wherein

the associated shape of each segment is specified by a set of n values.

4. The method of claim 3, wherein the n values are used to specify n half-planes

that when intersected define the shape of the segment.

5. The method of claim 4 further comprising identifying n values for the third

segment based on at least one attribute of the first and second segments.

6. The method of claim 5, wherein identifying the n values comprises retrieving

the n values from a data storage based on the attribute of the first and second segments.

7. The method of claim 3, wherein n is the number of manufacturing directions.

8. The method of claim 3, wherein n is the number of directions for the sides of at

least one item in the design.

9. The method of claim 8, wherein at least two directions are neither parallel nor

perpendicular with respect to each other.

10. The method of claim 1, wherein an acute angle is an angle that is greater than 0°

but less than 90°.

11. A computer readable medium that stores a computer program for removing

acute angles from routes in a design layout, the computer program comprising sets of

instructions for:

a) selecting a route with a plurality of segments;

b) identifying an acute angle between first and second contiguous

segments of the route;

c) inserting a third segment between the first and second segments,

wherein the third segment has an associated shape that fills the. acute angle between the first

and second segments.

12. The computer readable medium of claim 11, wherein each segment has a length

and the length of the third segment is zero.

13. The computer readable medium of claim 12, wherein each segment has an

associated shape, wherein the associated shape of each segment is specified by a set of n

values.

14. The computer readable medium of claim 13, wherein the n values are used to

specify n half-planes that when intersected define the shape of the segment.

15. The computer readable medium of claim 14 further comprising a set of

instructions for identifying n values for the third segment based on at least one attribute of the

first and second segments.

16. The computer readable medium of claim 15, wherein the set of instructions for

identifying the n values comprises a set of instructions for retrieving the n values from a data

storage based on the attribute of the first and second segments.

17. The computer readable medium of claim 13, wherein n is the number of

manufacturing directions.

18. The computer readable medium of claim 13, wherein n is the number of

directions for the sides of at least one item in the design.

19. The computer readable medium of claim 18, wherein at least two directions are

neither parallel nor perpendicular with respect to each other.

20. The computer readable medium of claim 11, wherein an acute angle is an angle

that is greater than 0° but less than 90°.