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90-550: Autodesk 3ds Max , formerly 3D Studio and 3D Studio Max , is a professional 3D computer graphics program for making 3D animations , models , games and images . It is developed and produced by Autodesk Media and Entertainment . It has modeling capabilities and a flexible plugin architecture and must be used on the Microsoft Windows platform. It is frequently used by video game developers , many TV commercial studios, and architectural visualization studios. It

180-425: A scalar function of the parameter. These are typically used in image processing programs to tune the brightness and color curves. Three-dimensional control points are used abundantly in 3D modeling, where they are used in the everyday meaning of the word 'point', a location in 3D space. Multi-dimensional points might be used to control sets of time-driven values, e.g. the different positional and rotational settings of

270-495: A 3D model is formed from points called vertices that define the shape and form polygons . A polygon is an area formed from at least three vertices (a triangle). A polygon of n points is an n-gon. The overall integrity of the model and its suitability to use in animation depend on the structure of the polygons. Before rendering into an image, objects must be laid out in a 3D scene . This defines spatial relationships between objects, including location and size . Animation refers to

360-410: A NURBS object. For instance, if some curve is defined using a certain degree and N control points, the same curve can be expressed using the same degree and N+1 control points. In the process a number of control points change position and a knot is inserted in the knot vector. These manipulations are used extensively during interactive design. When adding a control point, the shape of the curve should stay

450-401: A circle exactly, but it is not exactly parametrized in the circle's arc length. This means, for example, that the point at t {\displaystyle t} does not lie at ( sin ⁡ ( t ) , cos ⁡ ( t ) ) {\displaystyle (\sin(t),\cos(t))} (except for the start, middle and end point of each quarter circle, since

540-775: A circle, but they cannot represent it exactly. Rational splines can represent any conic section—including the circle—exactly. This representation is not unique, but one possibility appears below: The order is three, since a circle is a quadratic curve and the spline's order is one more than the degree of its piecewise polynomial segments. The knot vector is { 0 , 0 , 0 , π / 2 , π / 2 , π , π , 3 π / 2 , 3 π / 2 , 2 π , 2 π , 2 π } {\displaystyle \{0,0,0,\pi /2,\pi /2,\pi ,\pi ,3\pi /2,3\pi /2,2\pi ,2\pi ,2\pi \}\,} . The circle

630-400: A control point. The values of the knots control the mapping between the input parameter and the corresponding NURBS value. For example, if a NURBS describes a path through space over time, the knots control the time that the function proceeds past the control points. For the purposes of representing shapes, however, only the ratios of the difference between the knot values matter; in that case,

720-534: A human face and a hand that had originally appeared in the 1971 experimental short A Computer Animated Hand , created by University of Utah students Edwin Catmull and Fred Parke . 3-D computer graphics software began appearing for home computers in the late 1970s. The earliest known example is 3D Art Graphics , a set of 3-D computer graphics effects, written by Kazumasa Mitazawa and released in June 1978 for

810-485: A new knot span, a new control point becomes active, while an old control point is discarded. It follows that the values in the knot vector should be in nondecreasing order, so (0, 0, 1, 2, 3, 3) is valid while (0, 0, 2, 1, 3, 3) is not. Consecutive knots can have the same value. This then defines a knot span of zero length, which implies that two control points are activated at the same time (and of course two control points become deactivated). This has impact on continuity of

900-631: A number of reasons: Here, NURBS is mostly discussed in one dimension (curves); it can be generalized to two (surfaces) or even more dimensions. The order of a NURBS curve defines the number of nearby control points that influence any given point on the curve. The curve is represented mathematically by a polynomial of degree one less than the order of the curve. Hence, second-order curves (which are represented by linear polynomials) are called linear curves, third-order curves are called quadratic curves, and fourth-order curves are called cubic curves. The number of control points must be greater than or equal to

990-480: A particular degree can always be represented by a NURBS curve of higher degree. This is frequently used when combining separate NURBS curves, e.g., when creating a NURBS surface interpolating between a set of NURBS curves or when unifying adjacent curves. In the process, the different curves should be brought to the same degree, usually the maximum degree of the set of curves. The process is known as degree elevation . The most important property in differential geometry

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1080-580: A qualified educational institution. 3D computer graphics software 3-D computer graphics, contrary to what the name suggests, are most often displayed on two-dimensional displays. Unlike 3D film and similar techniques, the result is two-dimensional, without visual depth . More often, 3-D graphics are being displayed on 3-D displays , like in virtual reality systems. 3-D graphics stand in contrast to 2-D computer graphics which typically use completely different methods and formats for creation and rendering. 3-D computer graphics rely on many of

1170-425: A robot arm. NURBS surfaces are just an application of this. Each control 'point' is actually a full vector of control points, defining a curve. These curves share their degree and the number of control points, and span one dimension of the parameter space. By interpolating these control vectors over the other dimension of the parameter space, a continuous set of curves is obtained, defining the surface. The knot vector

1260-463: A scalar weight for each control point. This allows for more control over the shape of the curve without unduly raising the number of control points. In particular, it adds conic sections like circles and ellipses to the set of curves that can be represented exactly. The term rational in NURBS refers to these weights. The control points can have any dimensionality . One-dimensional points just define

1350-480: A special copy protection device (called a dongle ) to be plugged into the parallel port while the program was run, but later versions incorporated software based copy prevention methods instead. Current versions require online registration. Due to the high price of the commercial version of the program, Autodesk also offers a free student version, which explicitly states that it is to be used for "educational purposes only". The student version has identical features to

1440-761: A special case/subset of rational B-splines, where each control point is a regular non-homogenous coordinate [no 'w'] rather than a homogeneous coordinate . That is equivalent to having weight "1" at each control point; Rational B-splines use the 'w' of each control point as a weight . ) By using a two-dimensional grid of control points, NURBS surfaces including planar patches and sections of spheres can be created. These are parametrized with two variables (typically called s and t or u and v ). This can be extended to arbitrary dimensions to create NURBS mapping R n → R n {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} ^{n}} . NURBS curves and surfaces are useful for

1530-482: A surface in three-dimensional space . The shape of the surface is determined by control points . In a compact form, NURBS surfaces can represent simple geometrical shapes . For complex organic shapes, T-splines and subdivision surfaces are more suitable because they halve the number of control points in comparison with the NURBS surfaces. In general, editing NURBS curves and surfaces is intuitive and predictable. Control points are always either connected directly to

1620-401: A user to interpolate curved sections with straight geometry (for example a hole through a box shape). Although the surface tool is a useful way to generate parametrically accurate geometry, it lacks the "surface properties" found in the similar Edit Patch modifier, which enables a user to maintain the original parametric geometry whilst being able to adjust "smoothing groups" between faces. This

1710-535: A way to improve performance of the game engine or for stylistic and gameplay concerns. By contrast, games using 3D computer graphics without such restrictions are said to use true 3D. NURBS Non-uniform rational basis spline ( NURBS ) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces . It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes . It

1800-493: Is a basic method, in which one models something using only boxes, spheres, cones, cylinders and other predefined objects from the list of Predefined Standard Primitives or a list of Predefined Extended Primitives . One may also apply Boolean operations , including subtract, cut and connect. For example, one can make two spheres which will work as blobs that will connect with each other. These are called metaballs . Earlier versions (up to and including 3D Studio Max R3.1) required

1890-426: Is a class of 3-D computer graphics software used to produce 3-D models. Individual programs of this class are called modeling applications or modelers. 3-D modeling starts by describing 3 display models : Drawing Points, Drawing Lines and Drawing triangles and other Polygonal patches. 3-D modelers allow users to create and alter models via their 3-D mesh . Users can add, subtract, stretch and otherwise change

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1980-399: Is a mathematically exact representation of freeform surfaces like those used for car bodies and ship hulls, which can be exactly reproduced at any resolution whenever needed. With NURBS, a smooth sphere can be created with only one face. The non-uniform property of NURBS brings up an important point. Because they are generated mathematically, NURBS objects have a parameter space in addition to

2070-405: Is a sequence of parameter values that determines where and how the control points affect the NURBS curve. The number of knots is always equal to the number of control points plus curve degree plus one (i.e. number of control points plus curve order). The knot vector divides the parametric space in the intervals mentioned before, usually referred to as knot spans . Each time the parameter value enters

2160-460: Is a triangular function, nonzero over two knot spans rising from zero to one on the first, and falling to zero on the second knot span. Higher order basis functions are non-zero over corresponding more knot spans and have correspondingly higher degree. If u {\displaystyle u} is the parameter, and k i {\displaystyle k_{i}} is the i {\displaystyle i} knot, we can write

2250-582: Is a type of curve modeling , as opposed to polygonal modeling or digital sculpting . NURBS curves are commonly used in computer-aided design (CAD), manufacturing (CAM), and engineering (CAE). They are part of numerous industry-wide standards, such as IGES , STEP , ACIS , and PHIGS . Tools for creating and editing NURBS surfaces are found in various 3D graphics , rendering , and animation software packages. They can be efficiently handled by computer programs yet allow for easy human interaction. NURBS surfaces are functions of two parameters mapping to

2340-449: Is also used for movie effects and movie pre-visualization . 3ds Max features shaders (such as ambient occlusion and subsurface scattering ), dynamic simulation , particle systems , radiosity , normal map creation and rendering, global illumination , a customizable user interface , and its own scripting language . The original 3D Studio product was created for the DOS platform by

2430-410: Is composed of four quarter circles, tied together with double knots. Although double knots in a third order NURBS curve would normally result in loss of continuity in the first derivative, the control points are positioned in such a way that the first derivative is continuous. In fact, the curve is infinitely differentiable everywhere, as it must be if it exactly represents a circle. The curve represents

2520-404: Is computed as N i , n = f i , n N i , n − 1 + g i + 1 , n N i + 1 , n − 1 {\displaystyle N_{i,n}=f_{i,n}N_{i,n-1}+g_{i+1,n}N_{i+1,n-1}} f i {\displaystyle f_{i}} rises linearly from zero to one on

2610-471: Is easier to achieve if uniform B-splines are used. The definition of C continuity requires that the n th derivative of adjacent curves/surfaces ( d n C ( u ) / d u n {\displaystyle d^{n}C(u)/du^{n}} ) are equal at a joint. Note that the (partial) derivatives of curves and surfaces are vectors that have a direction and a magnitude; both should be equal. Highlights and reflections can reveal

2700-489: Is inspected by checking the quality of reflections of a neon-light ceiling on the car surface. This method is also known as "Zebra analysis". A NURBS curve is defined by its order, a set of weighted control points, and a knot vector. NURBS curves and surfaces are generalizations of both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points, which makes NURBS curves rational . ( Non-rational , aka simple , B-splines are

2790-432: Is known as parametric continuity . Parametric continuity of a given degree implies geometric continuity of that degree. First- and second-level parametric continuity (C and C¹) are for practical purposes identical to positional and tangential (G and G¹) continuity. Third-level parametric continuity (C²), however, differs from curvature continuity in that its parameterization is also continuous. In practice, C² continuity

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2880-412: Is mathematically expressed by the concept of geometric continuity . Higher-level tools exist that benefit from the ability of NURBS to create and establish geometric continuity of different levels: Geometric continuity mainly refers to the shape of the resulting surface; since NURBS surfaces are functions, it is also possible to discuss the derivatives of the surface with respect to the parameters. This

2970-433: Is not always possible while retaining the exact shape of the curve. In practice, a tolerance in the accuracy is used to determine whether a knot can be removed. The process is used to clean up after an interactive session in which control points may have been added manually, or after importing a curve from a different representation, where a straightforward conversion process leads to redundant control points. A NURBS curve of

3060-1254: Is obtained as the tensor product of two NURBS curves, thus using two independent parameters u {\displaystyle u} and v {\displaystyle v} (with indices i {\displaystyle i} and j {\displaystyle j} respectively): S ( u , v ) = ∑ i = 1 k ∑ j = 1 l R i , j ( u , v ) P i , j {\displaystyle S(u,v)=\sum _{i=1}^{k}\sum _{j=1}^{l}R_{i,j}(u,v)\mathbf {P} _{i,j}} with R i , j ( u , v ) = N i , n ( u ) N j , m ( v ) w i , j ∑ p = 1 k ∑ q = 1 l N p , n ( u ) N q , m ( v ) w p , q {\displaystyle R_{i,j}(u,v)={\frac {N_{i,n}(u)N_{j,m}(v)w_{i,j}}{\sum _{p=1}^{k}\sum _{q=1}^{l}N_{p,n}(u)N_{q,m}(v)w_{p,q}}}} as rational basis functions. A number of transformations can be applied to

3150-596: Is the curvature κ {\displaystyle \kappa } . It describes the local properties (edges, corners, etc.) and relations between the first and second derivative, and thus, the precise curve shape. Having determined the derivatives it is easy to compute κ = | r ′ ( t ) × r ″ ( t ) | | r ′ ( t ) | 3 {\displaystyle \kappa ={\frac {|r'(t)\times r''(t)|}{|r'(t)|^{3}}}} or approximated as

3240-633: Is the number of control points P i {\displaystyle \mathbf {P} _{i}} and w i {\displaystyle w_{i}} are the corresponding weights. The denominator is a normalizing factor that evaluates to one if all weights are one. This can be seen from the partition of unity property of the basis functions. It is customary to write this as C ( u ) = ∑ i = 1 k R i , n ( u ) P i {\displaystyle C(u)=\sum _{i=1}^{k}R_{i,n}(u)\mathbf {P} _{i}} in which

3330-1076: Is usually performed using 3-D computer graphics software or a 3-D graphics API . Altering the scene into a suitable form for rendering also involves 3-D projection , which displays a three-dimensional image in two dimensions. Although 3-D modeling and CAD software may perform 3-D rendering as well (e.g., Autodesk 3ds Max or Blender ), exclusive 3-D rendering software also exists (e.g., OTOY's Octane Rendering Engine , Maxon's Redshift) 3-D computer graphics software produces computer-generated imagery (CGI) through 3-D modeling and 3-D rendering or produces 3-D models for analytical, scientific and industrial purposes. There are many varieties of files supporting 3-D graphics, for example, Wavefront .obj files and .x DirectX files. Each file type generally tends to have its own unique data structure. Each file format can be accessed through their respective applications, such as DirectX files, and Quake . Alternatively, files can be accessed through third-party standalone programs, or via manual decompilation. 3-D modeling software

3420-610: The Apple II . 3-D computer graphics production workflow falls into three basic phases: The model describes the process of forming the shape of an object. The two most common sources of 3D models are those that an artist or engineer originates on the computer with some kind of 3D modeling tool , and models scanned into a computer from real-world objects (Polygonal Modeling, Patch Modeling and NURBS Modeling are some popular tools used in 3D modeling). Models can also be produced procedurally or via physical simulation . Basically,

3510-464: The FIRST competition for 3d animation are known to use 3ds Max. Polygon modeling is more common with game design than any other modeling technique as the very specific control over individual polygons allows for extreme optimization. Usually, the modeler begins with one of the 3ds max primitives, and using such tools as bevel and extrude , adds detail to and refines the model. Versions 4 and up feature

3600-610: The Yost Group , and published by Autodesk . The release of 3D Studio made Autodesk's previous 3D rendering package AutoShade obsolete. After 3D Studio DOS Release 4, the product was rewritten for the Windows NT platform, and renamed "3D Studio MAX." This version was also originally created by the Yost Group. It was released by Kinetix, which was at that time Autodesk's division of media and entertainment. Autodesk purchased

3690-407: The freeform curve of a ship's bow, could not be drawn with these tools. Although such curves could be drawn freehand at the drafting board, shipbuilders often needed a life-size version which could not be done by hand. Such large drawings were done with the help of flexible strips of wood, called splines. The splines were held in place at a number of predetermined points, by lead "ducks", named for

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3780-625: The spline curve or spline function. I. J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen. As computers were introduced into the design process, the physical properties of such splines were investigated so that they could be modelled with mathematical precision and reproduced where needed. Pioneering work was done in France by Renault engineer Pierre Bézier , and Citroën 's physicist and mathematician Paul de Casteljau . They worked nearly parallel to each other, but because Bézier published

3870-582: The 3D geometric space in which they are displayed. Specifically, an array of values called knots specifies the extent of influence of each control vertex (CV) on the curve or surface. Knots are invisible in 3D space and can't be manipulated directly, but occasionally their behavior affects the visible appearance of the NURBS object. Parameter space is one-dimensional for curves, which have only a single U dimension topologically, even though they exist geometrically in 3D space. Surfaces have two dimensions in parameter space, called U and V. NURBS curves and surfaces have

3960-507: The Autodesk logo, and the short name was again changed to "3ds Max" (upper and lower case), while the formal product name became the current "Autodesk 3ds Max." Many films have made use of 3ds Max, or previous versions of the program under previous names, in CGI animation, such as Avatar and 2012 , which contain computer generated graphics from 3ds Max alongside live-action acting. Mudbox

4050-466: The Editable Polygon object, which simplifies most mesh editing operations, and provides subdivision smoothing at customizable levels (see NURMS ). Version 7 introduced the edit poly modifier, which allows the use of the tools available in the editable polygon object to be used higher in the modifier stack (i.e., on top of other modifications). NURBS in 3ds Max is a legacy feature. None of

4140-451: The arclength from the second derivative κ = | r ″ ( s o ) | {\displaystyle \kappa =|r''(s_{o})|} . The direct computation of the curvature κ {\displaystyle \kappa } with these equations is the big advantage of parameterized curves against their polygonal representations. Non-rational splines or Bézier curves may approximate

4230-428: The bill-shaped protrusion that the splines rested against. Between the ducks, the elasticity of the spline material caused the strip to take the shape that minimized the energy of bending, thus creating the smoothest possible shape that fit the constraints. The shape could be adjusted by moving the ducks. In 1946, mathematicians started studying the spline shape, and derived the piecewise polynomial formula known as

4320-401: The boundaries of the intervals, the basis functions go smoothly to zero, the smoothness being determined by the degree of the polynomial. As an example, the basis function of degree one is a triangle function. It rises from zero to one, then falls to zero again. While it rises, the basis function of the previous control point falls. In that way, the curve interpolates between the two points, and

4410-652: The corresponding knot span and zero everywhere else. Effectively, N i , n {\displaystyle N_{i,n}} is a linear interpolation of N i , n − 1 {\displaystyle N_{i,n-1}} and N i + 1 , n − 1 {\displaystyle N_{i+1,n-1}} . The latter two functions are non-zero for n {\displaystyle n} knot spans, overlapping for n − 1 {\displaystyle n-1} knot spans. The function N i , n {\displaystyle N_{i,n}}

4500-418: The corresponding lower order basis functions are non-zero. By induction on n it follows that the basis functions are non-negative for all values of n {\displaystyle n} and u {\displaystyle u} . This makes the computation of the basis functions numerically stable. Again by induction, it can be proved that the sum of the basis functions for a particular value of

4590-447: The curve into disjoint parts and it would leave control points unused. For first-degree NURBS, each knot is paired with a control point. The knot vector usually starts with a knot that has multiplicity equal to the order. This makes sense, since this activates the control points that have influence on the first knot span. Similarly, the knot vector usually ends with a knot of that multiplicity. Curves with such knot vectors start and end in

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4680-506: The curve or surface, or else act as if they were connected by a rubber band. Depending on the type of user interface, the editing of NURBS curves and surfaces can be via their control points (similar to Bézier curves ) or via higher level tools such as spline modeling and hierarchical editing . Before computers, designs were drawn by hand on paper with various drafting tools . Rulers were used for straight lines, compasses for circles, and protractors for angles. But many shapes, such as

4770-429: The curve stays the same. A knot can be inserted multiple times, up to the maximum multiplicity of the knot. This is sometimes referred to as knot refinement and can be achieved by an algorithm that is more efficient than repeated knot insertion. Knot removal is the reverse of knot insertion. Its purpose is to remove knots and the associated control points in order to get a more compact representation. Obviously, this

4860-414: The curve. Typically, each point of the curve is computed by taking a weighted sum of a number of control points. The weight of each point varies according to the governing parameter. For a curve of degree d, the weight of any control point is only nonzero in d+1 intervals of the parameter space. Within those intervals, the weight changes according to a polynomial function ( basis functions ) of degree d. At

4950-431: The degree of the basis function. The parameter dependence is frequently left out, so we can write N i , n {\displaystyle N_{i,n}} . The definition of these basis functions is recursive in n {\displaystyle n} . The degree-0 functions N i , 0 {\displaystyle N_{i,0}} are piecewise constant functions . They are one on

5040-424: The editing of control points. The B-spline basis functions used in the construction of NURBS curves are usually denoted as N i , n ( u ) {\displaystyle N_{i,n}(u)} , in which i {\displaystyle i} corresponds to the i {\displaystyle i} -th control point, and n {\displaystyle n} corresponds with

5130-451: The fact that a single control point only influences those intervals where it is active is a highly desirable property, known as local support . In modeling, it allows the changing of one part of a surface while keeping other parts unchanged. Adding more control points allows better approximation to a given curve, although only a certain class of curves can be represented exactly with a finite number of control points. NURBS curves also feature

5220-410: The features have been updated since version 4 and have been ignored by the development teams over the past decade. For example, the updated path deform and the updated normalize spline modifiers in version 2018 do not work on NURBS curves anymore as they did in previous versions. An alternative to polygons, it gives a smoothed out surface that eliminates the straight edges of a polygon model. NURBS

5310-465: The final form. Some graphic art software includes filters that can be applied to 2D vector graphics or 2D raster graphics on transparent layers. Visual artists may also copy or visualize 3D effects and manually render photo-realistic effects without the use of filters. Some video games use 2.5D graphics, involving restricted projections of three-dimensional environments, such as isometric graphics or virtual cameras with fixed angles , either as

5400-423: The first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small startup company cooperating with Technische Universität Berlin . A surface under construction, e.g. the hull of a motor yacht, is usually composed of several NURBS surfaces known as NURBS patches (or just patches ). These surface patches should be fitted together in such a way that the boundaries are invisible. This

5490-559: The full version, but is only for single use and cannot be installed on a network. The student license expires after three years, at which time the user, if they are still a student, may download the latest version, thus renewing the license for another three years. In 2020, Autodesk had since reduced the free student version limit to 1 year only, as opposed to 3 years previously. In addition, all customers seeking free access to Autodesk educational products and services are required to provide proof of enrollment, employment, or contractor status at

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5580-411: The functions R i , n ( u ) = N i , n ( u ) w i ∑ j = 1 k N j , n ( u ) w j {\displaystyle R_{i,n}(u)={N_{i,n}(u)w_{i} \over \sum _{j=1}^{k}N_{j,n}(u)w_{j}}} are known as the rational basis functions . A NURBS surface

5670-817: The functions f {\displaystyle f} and g {\displaystyle g} as f i , n ( u ) = u − k i k i + n − k i {\displaystyle f_{i,n}(u)={\frac {u-k_{i}}{k_{i+n}-k_{i}}}} and g i , n ( u ) = 1 − f i , n ( u ) = k i + n − u k i + n − k i {\displaystyle g_{i,n}(u)=1-f_{i,n}(u)={\frac {k_{i+n}-u}{k_{i+n}-k_{i}}}} The functions f {\displaystyle f} and g {\displaystyle g} are positive when

5760-485: The geometrical interpretation, this means that the curve approaches the corresponding control point closely. In case of a double knot, the length of the knot span becomes zero and the peak reaches one exactly. The basis function is no longer differentiable at that point. The curve will have a sharp corner if the neighbour control points are not collinear. Using the definitions of the basis functions N i , n {\displaystyle N_{i,n}} from

5850-474: The important properties of not changing under the standard geometric affine transformations (Transforms), or under perspective projections. The CVs have local control of the object: moving a CV or changing its weight does not affect any part of the object beyond the neighboring CVs. (This property can be overridden by using the Soft Selection controls). Also, the control lattice that connects CVs surrounds

5940-460: The interval where N i , n − 1 {\displaystyle N_{i,n-1}} is non-zero, while g i + 1 {\displaystyle g_{i+1}} falls from one to zero on the interval where N i + 1 , n − 1 {\displaystyle N_{i+1,n-1}} is non-zero. As mentioned before, N i , 1 {\displaystyle N_{i,1}}

6030-415: The knot vectors (0, 0, 1, 2, 3, 3) and (0, 0, 2, 4, 6, 6) produce the same curve. The positions of the knot values influences the mapping of parameter space to curve space. Rendering a NURBS curve is usually done by stepping with a fixed stride through the parameter range. By changing the knot span lengths, more sample points can be used in regions where the curvature is high. Another use is in situations where

6120-404: The mesh to their desire. Models can be viewed from a variety of angles, usually simultaneously. Models can be rotated and the view can be zoomed in and out. 3-D modelers can export their models to files , which can then be imported into other applications as long as the metadata are compatible. Many modelers allow importers and exporters to be plugged-in , so they can read and write data in

6210-539: The mid-level, or Autodesk Combustion , Digital Fusion , Shake at the high-end. Match moving software is commonly used to match live video with computer-generated video, keeping the two in sync as the camera moves. Use of real-time computer graphics engines to create a cinematic production is called machinima . Not all computer graphics that appear 3D are based on a wireframe model . 2D computer graphics with 3D photorealistic effects are often achieved without wire-frame modeling and are sometimes indistinguishable in

6300-402: The native formats of other applications. Most 3-D modelers contain a number of related features, such as ray tracers and other rendering alternatives and texture mapping facilities. Some also contain features that support or allow animation of models. Some may be able to generate full-motion video of a series of rendered scenes (i.e. animation ). Computer aided design software may employ

6390-411: The order of the curve. In practice, cubic curves are the ones most commonly used. Fifth- and sixth-order curves are sometimes useful, especially for obtaining continuous higher order derivatives, but curves of higher orders are practically never used because they lead to internal numerical problems and tend to require disproportionately large calculation times. The control points determine the shape of

6480-450: The parameter is unity. This is known as the partition of unity property of the basis functions. The figures show the linear and the quadratic basis functions for the knots {..., 0, 1, 2, 3, 4, 4.1, 5.1, 6.1, 7.1, ...} One knot span is considerably shorter than the others. On that knot span, the peak in the quadratic basis function is more distinct, reaching almost one. Conversely, the adjoining basis functions fall to zero more quickly. In

6570-459: The parameter value has some physical significance, for instance if the parameter is time and the curve describes the motion of a robot arm. The knot span lengths then translate into velocity and acceleration, which are essential to get right to prevent damage to the robot arm or its environment. This flexibility in the mapping is what the phrase non uniform in NURBS refers to. Necessary only for internal calculations, knots are usually not helpful to

6660-443: The perfect smoothing, which is otherwise practically impossible to achieve without NURBS surfaces that have at least G² continuity. This same principle is used as one of the surface evaluation methods whereby a ray-traced or reflection-mapped image of a surface with white stripes reflecting on it will show even the smallest deviations on a surface or set of surfaces. This method is derived from car prototyping wherein surface quality

6750-499: The physical model can match the virtual model. William Fetter was credited with coining the term computer graphics in 1961 to describe his work at Boeing . An early example of interactive 3-D computer graphics was explored in 1963 by the Sketchpad program at Massachusetts Institute of Technology's Lincoln Laboratory . One of the first displays of computer animation was Futureworld (1976), which included an animation of

6840-876: The previous paragraph, a NURBS curve takes the following form: C ( u ) = ∑ i = 1 k N i , n ( u ) w i ∑ j = 1 k N j , n ( u ) w j P i = ∑ i = 1 k N i , n ( u ) w i P i ∑ i = 1 k N i , n ( u ) w i {\displaystyle C(u)=\sum _{i=1}^{k}{\frac {N_{i,n}(u)w_{i}}{\sum _{j=1}^{k}N_{j,n}(u)w_{j}}}\mathbf {P} _{i}={\frac {\sum _{i=1}^{k}{N_{i,n}(u)w_{i}\mathbf {P} _{i}}}{\sum _{i=1}^{k}{N_{i,n}(u)w_{i}}}}} In this, k {\displaystyle k}

6930-399: The product at the second release update of the 3D Studio MAX version and internalized development entirely over the next two releases. Later, the product name was changed to "3ds max" (all lower case) to better comply with the naming conventions of Discreet , a Montreal-based software company which Autodesk had purchased. When it was re-released (release 7), the product was again branded with

7020-628: The render engine how to treat light when it hits the surface. Textures are used to give the material color using a color or albedo map, or give the surface features using a bump map or normal map . It can be also used to deform the model itself using a displacement map . Rendering converts a model into an image either by simulating light transport to get photo-realistic images, or by applying an art style as in non-photorealistic rendering . The two basic operations in realistic rendering are transport (how much light gets from one place to another) and scattering (how surfaces interact with light). This step

7110-546: The rendered image, a model's data is contained within a graphical data file. A 3-D model is a mathematical representation of any three-dimensional object; a model is not technically a graphic until it is displayed. A model can be displayed visually as a two-dimensional image through a process called 3-D rendering , or it can be used in non-graphical computer simulations and calculations. With 3-D printing , models are rendered into an actual 3-D physical representation of themselves, with some limitations as to how accurately

7200-454: The representation is symmetrical). This would be impossible, since the x coordinate of the circle would provide an exact rational polynomial expression for cos ⁡ ( t ) {\displaystyle \cos(t)} , which is impossible. The circle does make one full revolution as its parameter t {\displaystyle t} goes from 0 to 2 π {\displaystyle 2\pi } , but this

7290-421: The resulting curve is a polygon, which is continuous , but not differentiable at the interval boundaries, or knots. Higher degree polynomials have correspondingly more continuous derivatives. Note that within the interval the polynomial nature of the basis functions and the linearity of the construction make the curve perfectly smooth, so it is only at the knots that discontinuity can arise. In many applications

7380-405: The resulting curve or its higher derivatives; for instance, it allows the creation of corners in an otherwise smooth NURBS curve. A number of coinciding knots is sometimes referred to as a knot with a certain multiplicity . Knots with multiplicity two or three are known as double or triple knots. The multiplicity of a knot is limited to the degree of the curve; since a higher multiplicity would split

7470-433: The results of his work, Bézier curves were named after him, while de Casteljau's name is only associated with related algorithms. NURBS were initially used only in the proprietary CAD packages of car companies. Later they became part of standard computer graphics packages. Real-time, interactive rendering of NURBS curves and surfaces was first made commercially available on Silicon Graphics workstations in 1989. In 1993,

7560-400: The same algorithms as 2-D computer vector graphics in the wire-frame model and 2-D computer raster graphics in the final rendered display. In computer graphics software, 2-D applications may use 3-D techniques to achieve effects such as lighting , and similarly, 3-D may use some 2-D rendering techniques. The objects in 3-D computer graphics are often referred to as 3-D models . Unlike

7650-432: The same fundamental 3-D modeling techniques that 3-D modeling software use but their goal differs. They are used in computer-aided engineering , computer-aided manufacturing , Finite element analysis , product lifecycle management , 3D printing and computer-aided architectural design . After producing a video, studios then edit or composite the video using programs such as Adobe Premiere Pro or Final Cut Pro at

7740-439: The same, forming the starting point for further adjustments. A number of these operations are discussed below. As the term suggests, knot insertion inserts a knot into the knot vector. If the degree of the curve is n {\displaystyle n} , then n − 1 {\displaystyle n-1} control points are replaced by n {\displaystyle n} new ones. The shape of

7830-432: The surface. This is known as the convex hull property. Surface tool was originally a 3rd party plugin, but Kinetix acquired and included this feature since version 3.0. The surface tool is for creating common 3ds Max splines, and then applying a modifier called "surface." This modifier makes a surface from every three or four vertices in a grid. It is often seen as an alternative to "mesh" or "nurbs" modeling, as it enables

7920-405: The temporal description of an object (i.e., how it moves and deforms over time. Popular methods include keyframing , inverse kinematics , and motion-capture ). These techniques are often used in combination. As with animation, physical simulation also specifies motion. Materials and textures are properties that the render engine uses to render the model. One can give the model materials to tell

8010-406: The users of modeling software. Therefore, many modeling applications do not make the knots editable or even visible. It's usually possible to establish reasonable knot vectors by looking at the variation in the control points. More recent versions of NURBS software (e.g., Autodesk Maya and Rhinoceros 3D ) allow for interactive editing of knot positions, but this is significantly less intuitive than

8100-537: Was also used in the final texturing of the set and characters in Avatar, with 3ds Max and Mudbox being closely related. 3ds Max has been used in the development of 3D computer graphics for a number of video games . Architectural and engineering design firms use 3ds Max for developing concept art and previsualization . Educational programs at secondary and tertiary level use 3ds Max in their courses on 3D computer graphics and computer animation . Students in

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