Abstract: A method of displaying text on a path includes creating a mapping between distances along the path and points on a line based on changes in direction of the path, composing glyphs on the line, having a total line length defined in accordance with the mapping, to form a composed line, associating the glyphs with the path in accordance with the mapping and the composed line, and outputting the association of the glyphs with the path for display of the glyphs along the path.

Abstract: Methods and apparatus for interactive curve-based freeform deformation of three-dimensional (3-D) models may provide a user interface that allows a user to interactively deform 3-D models based on simple and intuitive manipulations of a curve drawn on the model (i.e., freeform deformation). The user may apply freeform deformations using touch and/or multitouch gestures to specify and manipulate a deformation curve. The deformations may be applied by deforming the space around a curve/sweep path and deforming the 3-D model accordingly. The freeform deformation methods are not dependent on manipulation of a fixed set of parameters to perform deformations, and may provide for both local and global deformation. One or more weights and user interface elements for controlling those weights may be provided that allow the user to control the extent (region of influence) of the freeform deformations along the curve and/or perpendicular to the curve.

Abstract: Provenance techniques are disclosed for managing a history of a meeting. For example, a method for managing a history associated with a meeting comprises the following steps. Data associated with the meeting is collected. Provenance data is generated based on at least a portion of the collected data, wherein the provenance data is indicative of a lineage of one or more data items. A provenance graph is generated that defines a visual representation of the generated provenance data, wherein graph elements comprise one or more nodes and one or more edges between nodes, wherein nodes of the graph represent records associated with the collected data and edges of the graph represent relations between the records. One or more applications are associated with at least one graph element and are selectable to invoke functionality. The generated provenance graph is stored in a repository for use in analyzing the meeting.

Abstract: A graphics processing system includes a central processing unit that processes a cubic Bezier curve corresponding to a filled cubic Bezier path. Additionally, the graphics processing system includes a cubic preprocessor coupled to the central processing unit that formats the cubic Bezier curve to provide a formatted cubic Bezier curve having quadrilateral control points corresponding to a mathematically simple cubic curve. The graphics processing system further includes a graphics processing unit coupled to the cubic preprocessor that employs the formatted cubic Bezier curve in rendering the filled cubic Bezier path. A rendering unit and a display cubic Bezier path filling method are also provided.

Abstract: A method and system for approximating a curve, and a graphic display control method and apparatus are disclosed. The method for approximating a curve comprises the steps of acquiring number information of subdividing points for subdividing a curve needed to be approximated based on coordinate information of control points of the curve, acquiring coordinate information of the subdividing points based on the number information of the subdividing points and the coordinate information of the control points, and connecting the subdividing points with straight lines based on the coordinate information of the subdividing points. The invention could achieve efficient curve approximation and in turn achieve efficient graphic-display control.

Abstract: Parametric curve fitting using maximum curvature techniques are described. In one or more implementations, a parametric curve is fit to a segment of a plurality of data points that includes a first data point disposed between second and third data points by setting a point of maximum curvature for the segment of the curve at the first data point. A result of the fitting is output by the computing device.

Abstract: A target selection apparatus capable of quickly carrying out selection processing when selecting a desired target according to a target detection result and carrying out image processing on the target. An image corresponding to image data is displayed on a display unit. A drawing line is drawn on the image displayed on the display unit. A target included in the image data is selected based on the drawing line. In response to the drawing line becoming a closed curve, the selected target is determined.

Abstract: A display device and a method for controlling the same are disclosed. Herein, the method for controlling a display device is designed to include the steps of outputting a first Graphical User Interface (GUI), receiving a curvature change signal of a display screen outputting the first GUI, changing a curvature of the display screen based upon the received signal, generating a second GUI based upon GUI change data corresponding to the changed curvature of the display screen, and outputting the generated second GUI on the display screen.

Abstract: A system of curve generation takes a sequence of control points and constraint codes for each control point, and outputs a curve in which each of the constraints is satisfied. The set of constraints is chosen from the tangent angle, curvature, first derivative of curvature, and second derivative of curvature. The interactive curve design uses as its primitive, a curve whose curvature is a polynomial function of arclength (whose intrinsic equation is a polynomial). At each control point, a choice of G2 curvature continuity (tangent angle and curvature) or G4 curvature continuity (tangent angle and curvature plus first and second derivatives of curvature are continuous) is input. The desired curve is expressed as the solution to the chosen set of constraints.

Abstract: A machine-implemented process for determining, scaling, providing, and presenting comparative information in an accurate, scaled, useful, easily recognized, and understandable manner, including: reading the data sets; setting first and second boundaries of a first reference axis using first coordinates of data points of one data set having maximum and minimum values, respectively; setting first and second boundaries of each of the other reference axes by adjusting either the first coordinate of one data point of the selected data set having a maximum value or the first coordinate of one data point of the selected data set having a minimum value, wherein every E-value calculated based on the thus-obtained final first and second boundaries of the each of the other reference axes is substantially equal to an E-value of the first data set; and plotting the data points of the data sets. An electronic device capable of presenting a multiple-axis graph is also disclosed.

Abstract: Provided are a method, an apparatus and a system for dense graph simplification, and a recording medium for the same. The method includes receiving an original graph and extracting a plurality of salient points, which minimize a cost representing a greatest vertical distance between the original graph and each of a plurality of lines connecting two data points in a designated region on the original graph; and outputting a simplified graph in which the extracted salient points are connected. Thus, optimal results are ensured in dense graph simplification, and interactive control is allowed for a user.

Abstract: A method is provided for rendering pixels based on a certain type of Bézier curve, called a simple Bézier arch. The method uses an implicit function to determine whether each pixel in a domain triangle containing the arch is on the arch, on one side of the arch, or on the other side. The function's parameters can be linearly interpolated to allow efficient rendering of the triangle by a GPU. A method is also provided for applying the aforementioned method to render pixels, based on a non-linear Bézier curve having at most four control points, by subdividing the curve into simple Bézier arches as necessary. A computing device for performing these methods is also provided.

Abstract: A system is disclosed. The system includes a processor configured to: receive a path in an artwork, the path having at least one corner; receive a selection of a patterned tile to apply to the path; and automatically generate a patterned corner tile corresponding to the selected patterned tile at least in part by mapping a side patterned tile to a corner patterned tile; and a memory coupled to the processor and configured to provide the processor with instructions.

Abstract: An input stroked curve that is received by a graphics processing system can be rendering using at least two, and preferably more, rendering processes that are available for use by the system. The process or processes that are used for rendering the received stroked curve are selected based on whether the input stroked curve comprises one or more regions having a particular characteristic or characteristics, e.g. whether the input stroked curve comprises one or more self-overlapping regions. Preferably, the at least two rendering processes are each capable of correctly rendering different sets of stroked curves. Furthermore, the least two rendering process preferably differ in the processing burden that they place on the graphics processing system.

Abstract: When rendering a stroked curve for display in a graphics processing system, an input stroked curve 1 defined in user space 2 is received by the system. The portion of a canonical space 5 that corresponds to the received stroked curve 1 is determined by determining the portion of a canonical curve 12 defined in the canonical space 5 that corresponds to the received stroked curve 1. Then, for each of a plurality of sampling points within one or more primitives 4 that are generated to cover the received stroked curve 1? following its projection into surface space 3, it is determined whether a corresponding location in canonical space 5 (to the sampling point in surface space 3) is within the portion of the canonical space that corresponds to the received stroked curve, e.g. by looking up suitable information that has been stored (in advance) in one or more graphics textures. Data for rendering the received stroked curve 1 (e.g.

Abstract: A system and method of a gravity point drawing that simulate a physical model to draw or modify vector curves. A node is identified in a drawing of a graphical application. A size of a predefined space around the node and an intensity value associated with the node are determined. The intensity value affects the curvature of a vector curve in the predefined space. The vector curve is generated in the predefined space. The curvature of the vector curve is based on the size of the predefined space and the intensity value associated with the node in the drawing.

Abstract: Display methods and interfaces for high dynamic range images. High dynamic range images and corresponding histograms are displayed on a display device. The histogram panel displays low dynamic range and high dynamic range data of the images simultaneously. The low dynamic range and high dynamic range data is brightness level of the image pixels.

Abstract: This patent relates to thin plate spline (TPS)-based interpolation techniques for representing free-flowing vector graphics (VG) images based on user-specified features, such as points and curves. One or more features can be identified in a pixel grid. A higher-order least squares interpolating function with a TPS smoothness objective can then be utilized to interpolate individual color values to individual pixels of the pixel grid. Smoothness terms of the function that impose smoothness penalties can be interrupted in certain regions of the pixel grid based on attributes of the user-specified features. For example, a curve attribute can specify a particular color value(s), add or remove a smoothness penalty, or anisotropically impose a first derivative constraint in a particular direction.

Abstract: Methods, apparatuses, and computer program products are provided for facilitating visualization and analysis of medical data. A method may include accessing a first set of data points. The method may further include plotting a plurality of data points from the first set of data points on a first graph. The method may additionally include causing the first graph to be displayed. The method may also include accessing a second set of data points. The method may further include plotting a plurality of data points from the second set of data points on a second graph. The method may also include causing the second graph to be displayed overlaying the first graph. At least a portion of the second graph may be semi-transparent such that at least a portion of the first graph is viewable concurrently with the second graph. Corresponding apparatuses and computer program products are also provided.

Abstract: Systems and methods are described to render borders of controls and indicators in a graphical user interface (GUI), such that the rendered borders have continuous curvatures. In one aspect, a method includes generating a border of a GUI element to be represented in a GUI. The border includes a first straight side, a second straight side, and a corner portion that joins together the first straight side and the second straight side, such that a portion of the border that includes the first straight side, the corner portion and the second straight side is continuous and has continuous curvature. Additionally, the method includes representing the GUI element in the GUI.

Abstract: A vector image drawing device has the following configuration. A contour generation unit (104), based on vector data, generates contour data that represents the starting pixels on a scan line in a drawing area where fill-in starts, and the ending pixels where fill-in ends. An outline buffer (106) stores the number of starting or ending pixels in the contour data for fill-in for each drawn pixel. An error judgment unit (2), when storing the contour data in the outline buffer (106), determines in which pixel there is overflow in the outline buffer of contour data. A pixel position transfer unit (3) adds the numerical value of the overflow portion of a pixel that the error judgment unit (2) determined to have overflow to the numerical value of contour data that corresponds to a pixel.

Abstract: A touch screen to smooth a moving trajectory of a touch unit input as a curved line and to display the moving trajectory, and a display method of the touch screen are provided. The display method of the touch screen may include sampling coordinates at touch points when a touch unit moves on a touch screen, determining whether a moving trajectory of the touch unit is a curved line according to inclination between the coordinates, and fitting the sampled coordinates to a curve and displaying the fitted curve on the touch screen upon determining that the moving trajectory of the touch unit is the curved line.

Abstract: Disclosed is a computer implemented method, computer program product, and apparatus to decorate visible attributes of a rendered avatar. A server may collect a first user profile of a first avatar, the first user profile having at least one interest of a user. Next, the server may receive a location of the first avatar, wherein the location is associated with a view to at least a second avatar. The server can identify the second avatar among a group of avatars visible with respect to the first avatar. Further, the server may read a target profile of the second avatar then determine whether the second user profile satisfies a criterion based on the first user profile and the target profile. In addition, the server may render a modified rendered avatar to a client, responsive to the determination that the target profile satisfies the criterion.

Abstract: A system and method processes frequency spectrum of a signal in an image file of a computing device. The system loads the frequency spectrum from a storage system of the computing device, and displays the frequency spectrum on a user interface of the computing device. The method sets parameters of an object spectrum curve to be processed in the frequency spectrum and enables accessional functions for processing the object spectrum curve. According to the input parameters and the enabled accessional functions, an output range of the object spectrum curve may be displayed, and spectrum data of the object spectrum curve within the output range from the frequency spectrum may be output into a predetermined form, and stores the predetermined form according to a predetermined storage path.

Abstract: A method, apparatus, system, and computer readable storage medium provide the ability to transition between two different profile curves in a swept surface extrusion. Each curve has section sequences that include consecutive sections, which in turn include constant attributes, which in turn include graphic attributes and semantic attributes. The section sequences define a semantic pattern for each profile curve. A globally optimal match is computed between the sections of the different curves. Adapted curves are generated that are structurally identical but geometrically resemble their respective original curves. An actual profile curve is computed for a given position on an extrusion line using a one-to-one vertex position morphing based on the adapted curves. The swept surface extrusion is performed and the result is displayed.

Abstract: Various embodiments for social networking influenced map generation are disclosed. One embodiment is a method for generating a map that comprises retrieving, by a computing device, location data from a mobile computing device. The method further comprises determining, by the computing device, at least one attribute corresponding to the mobile computing device according to the retrieved location data and retrieving, by the computing device, information relating to a messaging event occurring on the mobile computing device. The method further comprises generating, by the computing device, a map displaying a path of traversal of the mobile computing device based on the retrieved location data, the map further comprising at least one graphical representation relating to the messaging event, the at least one graphical representation being displayed on the path of traversal.

Abstract: A method for generating a high dynamic range (HDR) image from images of a scene obtained at one or more exposure values is disclosed. In this embodiment, one of the obtained images is selected as a reference image. Further, mapped images are obtained by mapping pixel intensity values to corresponding irradiance values in each image. Furthermore, a pixel intensity value dependent weighting factor is determined. Moreover, a set of images is identified from the mapped images for pixels in the reference image. Also, a set of corresponding mapped pixels is established for the mapped pixels in reference image in the set of images. Further, a similarity measure is computed for the mapped pixels of reference image and corresponding mapped pixels in the set of images. Furthermore, each mapped pixel of the reference image is combined with a subset of its established corresponding mapped pixels in the set of images.

Abstract: A device includes a processor which executes a process including generating data of a second graphic identified by shifting each of first sides of a first graphic by a length in a direction toward an inside of the first graphic and by tracing, in a direction, the first sides after the shifting and intersection points between the first sides after the shifting, generating data of a third graphic by shifting each of second sides of the second graphic to both sides of each of the second side by the length and by linking end points of the second sides after the shifting using a circular arc which is centered on an end point of the second side before the shifting and which has a radius of the length, and generating data of a fourth graphic by performing a logical addition operation between the second graphic and the third graphic.

Abstract: Ink rendering techniques are described. In an implementation, an input is recognized by one or more modules that are executable on one or more processors of a computing device as an ink stroke to be rendered by a display device of the computing device. The ink stroke is built by the one or more modules using a strip of triangles and the strip of triangles is sent to a graphics processing unit to render the ink stroke.

Abstract: A system is disclosed. The system includes a processor configured to: receive a path in an artwork, the path having at least one corner; receive a selection of a patterned tile to apply to the path; and automatically generate a patterned corner tile corresponding to the selected patterned tile at least in part by mapping a side patterned tile to a corner patterned tile; and a memory coupled to the processor and configured to provide the processor with instructions.

Abstract: A method and system for computer aided design (CAD) is disclosed for designing geometric objects, wherein interpolation and/or blending between such objects is performed while deformation data is being input. Thus, a designer obtains immediate feedback to input modifications without separately entering a command(s) for performing such deformations. A novel N-sided surface generation technique is also disclosed herein to efficiently and accurately convert surfaces of high polynomial degree into a collection of lower degree surfaces. E.g., the N-sided surface generation technique disclosed herein subdivides parameter space objects (e.g., polygons) of seven or more sides into a collection of subpolygons, wherein each subpolygon has a reduced number of sides. More particularly, each subpolygon has 3 or 4 sides. The present disclosure is particularly useful for designing the shape of surfaces. Thus, the present disclosure is applicable to various design domains such as the design of, e.g.

Abstract: The document data (e.g., conference materials) are transmitted from a conference server apparatus to a terminal apparatus 3 attending a teleconference, and the terminal apparatus 3 utilizes a displaying unit 46 to display the document data on the lower layer, utilizes a accepting unit 45 (e.g., a pen tablet or a mouse) to accept a writing operation performed on the display screen, generates a write-image regarding the writing operation on a layer upper than the lower layer, and displays and overlays the generated write-image on the document data. At that time, the terminal apparatus 3 sets a rectangular write-inhibition area containing character or word included in the sentence of document data. For example, when a leader line is written inside the write-inhibition area, an image regarding the written leader line is displayed outside the write-inhibition area.

Abstract: The present disclosure includes, among other things, systems, methods and program products for application of bevel curves to splines.

Abstract: A recently rendered section of a curve is redrawn to smooth the curve on-the-fly while a user moves a stylus or other input device. On receiving data points for the curve, an old rendered section for prior data points is deleted by curve redrawing code, and a new spline that's visually smooth through the new data points and at least one prior data point is added. “Visually smooth” is defined using tangents. The rendered spline is a cardinal or other cubic Hermite spline. The curve is redrawn for display by overwriting frame buffer data. A single instruction multiple data processing architecture simultaneously calculates multiple data points for the new section of the curve rendering. A digital ink rendering uses a pen-tip shape or an arc shape, based on data point locations. The pen-tip shape simulates a square-tip pen, highlighter, pencil, charcoal, paintbrush, or liquid ink pen.

Abstract: A graph display apparatus including: a display unit; a graph formula input unit for receiving input of a graph formula; a coordinate system setting unit for setting a display range of a coordinate system and a scale interval on a coordinate axis in the coordinate system; a coordinate system display controlling unit for making the display unit display the coordinate axis, and display scales and scale values at the scale interval, the coordinate system display controlling unit including a scale value display controlling unit for detecting overlapping of the scale values to be displayed, and, when the scale values overlap, making the display unit display only scale values of scales at both ends among the scales to be displayed on the coordinate axis; and a graph display controlling unit for making the display unit display a graph of the graph formula.

Abstract: A lighting module of a hair/fur pipeline may be used to produce lighting effects in a lighting phase for a shot and an optimization module may be used to: determine if a cache hair state file including hair parameters exists; and determine if the cache hair state file includes matching hair parameters to be used in the shot, and if so, the hair parameter values from the cache hair state file are used in the lighting phase.

Abstract: A system of curve generation takes a sequence of control points and constraint codes for each control point, and outputs a curve in which each of the constraints is satisfied. The set of constraints is chosen from the tangent angle, curvature, first derivative of curvature, and second derivative of curvature. The interactive curve design uses as its primitive, a curve whose curvature is a polynomial function of arclength (whose intrinsic equation is a polynomial). At each control point, a choice of G2 curvature continuity (tangent angle and curvature) or G4 curvature continuity (tangent angle and curvature plus first and second derivatives of curvature are continuous) is input. The desired curve is expressed as the solution to the chosen set of constraints.

Abstract: A computer implemented method and apparatus for reproducing an input curve on a mobile device comprising detecting the input curve, sampling the input curve into a discrete set of vertices, performing a normalized dot product of an edge leading into each one of the discrete set of vertices and a tangent to an edge leading from each one of the discrete set of vertices, setting one or more spline stiffness parameter based on the normalized dot product corresponding to each vertex; and converting the sampled input curve into one or more spline patch with the set spline stiffness parameter corresponding to each vertex.

Abstract: A complex curved primitive is decomposed into curvy RHTs comprising a curved portion and horizontal and vertical lines. Pixel rows covered by curvy RHTs are determined. RHT pixels covered by the curved primitive are determined with counters. Tile based color rendering is performed for covered pixels. The primitive path is decomposed into Bezier curves. Curvy RHTs may overlap and may cover pixels that are not covered by the curved primitive. Pixel rows are located by traversing an RHT path and the direction of traversing may determine pixel counts. Pixel coverage and tile coverage information is stored in memory. Pixels may be rendered in parallel. The curved primitive is rendered in a tile binning phase and a tile rendering phase. Tile rendering comprises a pixel coverage first pass which determines pixels covered by said curved primitive and a color rendering second pass.

Abstract: Various embodiments are directed to methods for marketing investment services. The methods may comprise receiving at least one signal from a position detector indicating a position of a viewer relative to a display screen in a first axis and a perpendicular distance of the viewer from the display screen. The display screen may be aligned along the first axis and a second axis. The methods may also comprise displaying with the display screen a user interface. The user interface may comprise an age scale aligned with the first axis, an asset scale aligned with a second axis and a chart of assets versus age. Upon determining that the perpendicular distance of the viewer from the display screen is less than a predetermined value, the methods may comprise modifying the interface to display an element at a first position on the age scale corresponding to a position of the viewer relative to the display screen in the first axis.

Abstract: A system and associated method for hierarchically decomposing a workflow graph G into a process structure tree PST. The workflow graph G is a two-terminal graph parsed into a tree T having triconnected components. Boundary pairs of all triconnected components in T are computed and fragments are discovered with boundary pairs. T is restructured into PST pursuant to categories of triconnected components in T. PST is deterministic and modular. PST represents a block-based process model that has fine blocks of execution units. PST is computed in time linear to the number of edges in G.

Abstract: Provenance techniques are disclosed for managing a history of a meeting. For example, a method for managing a history associated with a meeting comprises the following steps. Data associated with the meeting is collected. Provenance data is generated based on at least a portion of the collected data, wherein the provenance data is indicative of a lineage of one or more data items. A provenance graph is generated that defines a visual representation of the generated provenance data, wherein graph elements comprise one or more nodes and one or more edges between nodes, wherein nodes of the graph represent records associated with the collected data and edges of the graph represent relations between the records. One or more applications are associated with at least one graph element and are selectable to invoke functionality. The generated provenance graph is stored in a repository for use in analyzing the meeting.

Abstract: One embodiment of the present invention sets forth a technique for stroking rendered paths. Path rendering may be accelerated when a graphics processing unit or other processor is configured to identify pixels that are within half of the stroke width of any point along a path to be stroked. The path is represented by quadratic Bèzier segments and a cubic equation is evaluated to determine whether or not each point in a conservative hull that bounds the quadratic Bèzier segment is within the stroke width.

Abstract: An apparatus for marketing investment services comprising a display screen aligned along a vertical axis and a horizontal axis, a position detector, and a computer device. The computer device may receive at least one signal from the position detector indicating a position of a viewer relative to the display screen in the horizontal axis and a perpendicular distance of the viewer from the display screen; cause the display screen to display a user interface. The user interface may comprise an age scale aligned with the horizontal axis, an asset scale aligned with the vertical axis and a chart of assets versus age. Upon determining that the perpendicular distance of the viewer from the display screen is less than a predetermined value, the computer device modify the interface to display an element at a first position on the age scale corresponding to a position of the viewer relative to the display screen in the horizontal axis.

Abstract: An image processing apparatus measures duration of the drawing operation by using coordinate information that indicates coordinate instructed to draw and time information that indicates time when the coordinates are detected, determines predicted time in accordance with the duration of the drawing operation, and generates an drawn image by calculating the predicted coordinates after the predicted time passes. The image processing apparatus calculates a characteristic value of the drawing operation by using the coordinate information and the time information and measures the duration of the drawing operation in case the characteristic value of the drawing operation is less than predetermined threshold value.

Abstract: One embodiment of the present invention sets forth a technique for subdividing stroked higher-order curved segments into quadratic Bèzier curve segments. Path stroking may be accelerated when a GPU or other processor is configured to perform the subdivision operations. Cubic Bèzier path segments are subdivided into quadratic Bèzier curve segments and other lower-order segments at key features. The quadratic Bèzier curve segments approximate the cubic Bèzier path segments. A variance metric is computed for each quadratic Bèzier curve segment, and when the variance metric indicates that the quadratic Bèzier curve segment deviates by more than a threshold from the corresponding portion of the cubic Bèzier path segment, the quadratic Bèzier curve segment is further subdivided. The path composed of the quadratic Bèzier curve segments is then stroked by rendering hull geometry that encloses the path.

Abstract: Methods and apparatus for generating an n-sided patch by sketching on a three-dimensional reference surface. A user draws a closed curve on a 3D surface; the drawn outline is taken as a boundary for an N-sided patch. If the user does not close the curve, the system may automatically close the curve, as a closed outer boundary curve may be required to produce an N-sided patch. The boundary conditions, the positions, and the surface normals at the boundary are inferred automatically from the 3D surface that the user has drawn the curve on. In addition, boundary curves for the same patch may be drawn on different 3D shapes; multiple 3D shapes may be used as the template or canvas on which the user draws curves from which a patch is to be generated.

Abstract: Methods and apparatus provide for a moderator that defines an editing space providing access to multiple applications. The moderator associates a first portion of the editing space with a first application and aligns the editing space over a work area of the first application. The moderator creates first content with the first application through the first portion of the editing space, such that the first content is bounded according to the dimension of the first portion of the editing space. The moderator further associates a second portion of the editing space with a second application. The moderator aligns the editing space over a work area of the second application. The moderator creates second content in the second application through the second portion of the editing space as the editing space displays the representation of the saved first content in the first portion of the editing space.

Abstract: A trace guide (TG) that has been set within a manual trace reference cross-section (58) is illustrated with a dashed line. The trace guide (TG) is obtained from three-dimensional contour information based on already-completed manual tracing of a first sheet. Therefore, the user draws a trace line (TL) corresponding to the contour of target tissue on a second sheet of the manual trace reference cross-section (58) while referring to the trace guide (TG) and also checking a tomographic image of the target tissue within the manual trace reference cross-section (58). The user may: draw the trace line (TL) in full; use apart of the trace guide (TG) without alteration as the trace line (TL) and correct the remaining part to serve as the trace line (TL); or use the trace guide (TG) without alteration as the trace line (TL).

Abstract: Systems and method for presenting a free-form drawing are described. In some aspects, a first point, a second point, and a third point from an input curve in the free-form drawing are received. A first quadratic Bezier curve is determined, where a control point of the first quadratic Bezier curve includes the second point and endpoints of the first quadratic Bezier curve include the first point and the third point. A first portion of the first quadratic Bezier curve is provided for display, where endpoints of the first portion of the first quadratic Bezier curve include the first point and a second terminal point, and where the first portion of the first quadratic Bezier curve does not include the third point.