Drawing3d documented Class Library

Utils Members

Utils overview

Public Static (Shared) Fields

big big is the same as double.MaxValue
bigI bigI is the same as int.MaxValue
DecimalSign Sets or gets the DecimalSeparator.
Delimiter Separates the coordiantes of a xyz-point, when it is converted to a string Defaultvalue is "/"
DoubleFormat This format is taken for all conversions from double to string. The default is "0.######".
epsilon The constant epsilon is used in the methods less and equals. It means the tolerance of these functions. The default value is 1e-10
small small is the same as double.MinValue
smallI smallI is the same as int.MinValue

Public Static (Shared) Methods

AngleOverloaded. Calculates the angle in radian between two vectors in a counterclockwise sense.
Bernstein Calculates the Bernstein coefficient of degree and index id at the value t. This is used for the calculation of Bezierfunction and Meshes
BernsteinDerive Calculate the derivation of the Bernstein coefficient of degree, index id at the value t.
CoeffSpline Returns the spline coefficients for a given parameter t from the interval[0,1] a knotsarray, a count of controlpoins and the degree
CoeffSplineEx Returns the spline coefficients and the derivated spline coefficients for a given parameter t from the interval[0,1] a knotsarray, a count of controlpoins and the degree
ColorXor Calculates the xored value of the Color C with ColorBack.
CombineAnd Combines the sorted arrays a and b by a logical "and". The first member of a (b) toggle the state to true, the second to false and so on. The result toggle to true only when both a and b have the state true. If one have the state false then the result toggles to false.
DefaultKnots Returns an array of ControlPointCount + Degree + 1 knots, which are not uniform. Example: KNOTS={0,0,0,0,1,2,2,2,2} for ControlPointCount=5 and Degree =3.
DegToRad Calculates the radian of a degreemeasure
EqualsOverloaded. This function checks the equality between two values. This is to avoid errors about computational accuracy with doubles. If their distance is less then epsilon, then equality is done.
FloatToStr Converts a floating value to a string by using DoubleFormat
funBezier retrieves the value of Bezierfunction at t. The degree is given by the count of "Points" in the array "Points".
funBezier3D Calculates the 3D-Points of a Bezier curve of degree 3 with controlpoints "Points".
funBezierDerive retrieves the first derive of Bezierfunction at t. The degree is 3;
funBezierDerive3D retrieves the first derive of 3D- Bezier curve at t. The degree is 3;
funBSpline2d Calculates the 2-dimensional spline. It returns a point to a given parameter t from the interval[0,1], the knots, the degree and the controlpoints
funBSpline3d Calculates the derivation of 3-dimensional spline. It returns a vactor to a given parameter t from the interval[0,1], the knots, the degree and the controlpoints
funBSplineDerived2d Calculates the 2-dimensional spline. It returns a point to a given parameter t from the interval[0,1], the knots, the degree and the controlpoints
funBSplineDerived3d Calculates the 3-dimensional spline. It returns a point to a given parameter t from the interval[0,1], the knots, the degree and the controlpoints
funNurbs2d Calculates the 2-dimensional nurbs. It returns a point to a given parameter t from the interval[0,1], the knots,the weights, the degree and the controlpoints
funNurbs3d Calculates the 3-dimensional nurbs. It returns a point to a given parameter t from the interval[0,1], the knots,the weights, the degree and the controlpoints
funNurbsDerive2d Calculates the the derivation of a 2-dimensional nurbs. It returns a tangent vector to a given parameter t from the interval[0,1], the knots,the weights, the degree and the controlpoints
funNurbsDerive3d Calculates the the derivation of a 3-dimensional nurbs. It returns a tangent vector to a given parameter t from the interval[0,1], the knots,the weights, the degree and the controlpoints
funQSpline retrieves the value of QSpline ( a quadratic weighted spline) at t. He is given by two points A and B and a controlpoint P. Additionally a weight for the attraction of the controlpoint can be set.
funQSpline3D retrieves the value of 3D- QSpline ( a quadratic weighted spline) at t. He is given by two points A and B and a controlpoint P. Additionally a weight for the attraction of the controlpoint can be set.
funQSplineDerive Retrieves the first derivation of a Qspline. See funQSpline.
funQSplineDerive3D Retrieves the first derivation of a 3D-Qspline. See funQSpline3D.
GetMaxRectangleOverloaded. Calculates a minimum rectangle containing R1 and R2
InsideRectangleOverloaded. Calculates whether a point is inside a rectangle or not.
Less This function controls, at which point a number is lower then an other, this means if the difference b - a is less than epsilon, then a is really less than b.
MaxRectOverloaded. Check the point xy and retrieves a rectangle, which contains the rectangle rect and the point xyz
Mesh Calculates a Bezier surface. It returns for to parameter u,v from [0,1] a 3D-Point. The array Points contains the Controlpoints. Hint : if the dimension of Points is greather than 4, a zero point will be returned.
MeshDeriveU Calculates the partial u-derivation of a Bezier surface. It returns for to parameter u,v from [0,1] a vector. The array Points contains the Controlpoints. Hint : if the dimension of Points is greather than 4, a zero point will be returned.
MeshDeriveV Calculates the partial v-derivation of a Bezier surface. It returns for to parameter u,v from [0,1] a vector. The array Points contains the Controlpoints. Hint : if the dimension of Points is greather than 4, a zero point will be returned.
N_over_K Returns the binomialcoefficient, with N over K. z.b.: N_over_K(6, 2) is 15;
OrderRect Order the values of a rectangle such that left < right and bottom < top
PolarUnit Calculates the points of a unit sphere, where Alpha indicates the geographical longitude and Phi the latitude. For the values Apha = 0 and Phi = 0 you get the Point(1, 0, 0). For an arbitrary sphere you have to multiply with it´s Radius
RadToDeg Converts Degree to Radian
RectNomalize represents the format in which a double value is converted to a string by FloatToStr This format is used by the overridden ToString-method of xyz, xy ..
Resetrectangle Rests a rectangle.
Round The classical round-method which returns an integer. This integer is the nearest integer to "value".
Spat Calculates the Spat-product which is defined by (a X b). c, where "X" is the cross product and "." is the dot product. It´s the same as the determinant of the Matrix, which has this vectors as columns.
StrToFloat Convert a string to float. Decpoint and deccomma are valid separators! By using this conversion you avoid a lot of troubles.
TransformRectangle Transforms a rectangle by a transformation.
trunc The classical trunc-method which returns an integer. This integer is the greatest integer lower than "value".
UniformKnots Returns an array of ControlPointCount + Degree + 1 knots, which are uniform. Example: KNOTS={0,1.125,0.25,0.375,0.5,0.625,0.75,0.875,1} for ControlPointCount=5 and Degree =3.
UnitToPolar Calculates the polar angles of a Point

Public Instance Constructors

Utils Constructor Initializes a new instance of the Utils class.

Public Instance Methods

Equals (inherited from Object)Overloaded.  
GetHashCode (inherited from Object) 
GetType (inherited from Object) 
ToString (inherited from Object) 

Protected Instance Methods

Finalize (inherited from Object) 
MemberwiseClone (inherited from Object) 

See Also

Utils Class | Drawing3d.Math Namespace