Struct Vector3D
3-element structure that can be used to represent positions in 3D space or any other pair of numeric values.
[Serializable]
public struct Vector3D : IEquatable<Vector3D>- Implements
- Inherited Members
- Extension Methods
Constructors
Vector3D(double, double, double)
Constructs a new Vector3D with the given components.
public Vector3D(double x, double y, double z)Parameters
xdoubleThe vector's X component.
ydoubleThe vector's Y component.
zdoubleThe vector's Z component.
Vector3D(int, int, int)
Constructs a new Vector3D with the given components.
public Vector3D(int x, int y, int z)Parameters
Vector3D(float, float, float)
Constructs a new Vector3D with the given components.
public Vector3D(float x, float y, float z)Parameters
xfloatThe vector's X component.
yfloatThe vector's Y component.
zfloatThe vector's Z component.
Fields
X
The vector's X component. Also accessible by using the index position [0].
public double XField Value
Y
The vector's Y component. Also accessible by using the index position [1].
public double YField Value
Z
The vector's Z component. Also accessible by using the index position [2].
public double ZField Value
Properties
Inf
Infinity vector, a vector with all components set to PositiveInfinity.
public static Vector3D Inf { get; }Property Value
- Vector3D
Equivalent to
new Vector3D(Math.Inf, Math.Inf, Math.Inf).
this[int]
Access vector components using their index.
public double this[int index] { readonly get; set; }Parameters
indexint
Property Value
Exceptions
- ArgumentOutOfRangeException
indexis not 0, 1 or 2.
One
One vector, a vector with all components set to 1.
public static Vector3D One { get; }Property Value
- Vector3D
Equivalent to
new Vector3D(1, 1, 1).
UnitX
Unit vector along the X axis: (1 0 0).
public static Vector3D UnitX { get; }Property Value
UnitY
Unit vector along the Y axis: (0 1 0).
public static Vector3D UnitY { get; }Property Value
UnitZ
Unit vector along the Z axis: (0 0 1).
public static Vector3D UnitZ { get; }Property Value
Zero
Zero vector, a vector with all components set to 0.
public static Vector3D Zero { get; }Property Value
- Vector3D
Equivalent to
new Vector3D(0, 0, 0).
Methods
Abs()
Returns a new vector with all components in absolute values (i.e. positive).
public readonly Vector3D Abs()Returns
- Vector3D
A vector with Abs(double) called on each component.
AngleTo(Vector3D)
Returns the unsigned minimum angle to the given vector, in radians.
public readonly double AngleTo(Vector3D to)Parameters
toVector3DThe other vector to compare this vector to.
Returns
- double
The unsigned angle between the two vectors, in radians.
BezierDerivative(Vector3D, Vector3D, Vector3D, double)
Returns the derivative at the given t on the Bezier curve defined by this vector
and the given control1, control2, and end points.
public readonly Vector3D BezierDerivative(Vector3D control1, Vector3D control2, Vector3D end, double t)Parameters
control1Vector3DControl point that defines the bezier curve.
control2Vector3DControl point that defines the bezier curve.
endVector3DThe destination value for the interpolation.
tdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
Returns
- Vector3D
The resulting value of the interpolation.
BezierInterpolate(Vector3D, Vector3D, Vector3D, double)
Returns the point at the given t on a one-dimensional Bezier curve defined by this vector
and the given control1, control2, and end points.
public readonly Vector3D BezierInterpolate(Vector3D control1, Vector3D control2, Vector3D end, double t)Parameters
control1Vector3DControl point that defines the bezier curve.
control2Vector3DControl point that defines the bezier curve.
endVector3DThe destination vector.
tdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
Returns
- Vector3D
The interpolated vector.
Ceiling()
Returns a new vector with all components rounded up (towards positive infinity).
public readonly Vector3D Ceiling()Returns
- Vector3D
A vector with Ceiling(double) called on each component.
Clamp(Vector3D, Vector3D)
Returns a new vector with all components clamped between the
components of min and max using
Clamp(double, double, double).
public readonly Vector3D Clamp(Vector3D min, Vector3D max)Parameters
minVector3DThe vector with minimum allowed values.
maxVector3DThe vector with maximum allowed values.
Returns
- Vector3D
The vector with all components clamped.
Cross(Vector3D)
Returns the cross product of this vector and with.
public readonly Vector3D Cross(Vector3D with)Parameters
withVector3DThe other vector.
Returns
- Vector3D
The cross product vector.
CubicInterpolate(Vector3D, Vector3D, Vector3D, double)
Performs a cubic interpolation between vectors preA, this vector,
b, and postB, by the given amount weight.
public readonly Vector3D CubicInterpolate(Vector3D b, Vector3D preA, Vector3D postB, double weight)Parameters
bVector3DThe destination vector.
preAVector3DA vector before this vector.
postBVector3DA vector after
b.weightdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
Returns
- Vector3D
The interpolated vector.
CubicInterpolateInTime(Vector3D, Vector3D, Vector3D, double, double, double, double)
Performs a cubic interpolation between vectors preA, this vector,
b, and postB, by the given amount weight.
It can perform smoother interpolation than CubicInterpolate(Vector3D, Vector3D, Vector3D, double)
by the time values.
public readonly Vector3D CubicInterpolateInTime(Vector3D b, Vector3D preA, Vector3D postB, double weight, double t, double preAT, double postBT)Parameters
bVector3DThe destination vector.
preAVector3DA vector before this vector.
postBVector3DA vector after
b.weightdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
tdoublepreATdoublepostBTdouble
Returns
- Vector3D
The interpolated vector.
Deconstruct(out double, out double, out double)
Helper method for deconstruction into a tuple.
public readonly void Deconstruct(out double x, out double y, out double z)Parameters
DirectionTo(Vector3D)
Returns the normalized vector pointing from this vector to to.
public readonly Vector3D DirectionTo(Vector3D to)Parameters
toVector3DThe other vector to point towards.
Returns
- Vector3D
The direction from this vector to
to.
DistanceSquaredTo(Vector3D)
Returns the squared distance between this vector and to.
This method runs faster than DistanceTo(Vector3D), so prefer it if
you need to compare vectors or need the squared distance for some formula.
public readonly double DistanceSquaredTo(Vector3D to)Parameters
toVector3DThe other vector to use.
Returns
- double
The squared distance between the two vectors.
DistanceTo(Vector3D)
Returns the distance between this vector and to.
public readonly double DistanceTo(Vector3D to)Parameters
toVector3DThe other vector to use.
Returns
- double
The distance between the two vectors.
- See Also
Dot(Vector3D)
Returns the dot product of this vector and with.
public readonly double Dot(Vector3D with)Parameters
withVector3DThe other vector to use.
Returns
- double
The dot product of the two vectors.
Equals(Vector3D)
Returns true if the vectors are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Vector3D) instead, which is more reliable.
public readonly bool Equals(Vector3D other)Parameters
otherVector3DThe other vector.
Returns
- bool
Whether or not the vectors are exactly equal.
Equals(object?)
Returns true if the vector is exactly equal
to the given object (obj).
Note: Due to floating-point precision errors, consider using
IsEqualApprox(Vector3D) instead, which is more reliable.
public override readonly bool Equals(object? obj)Parameters
objobjectThe object to compare with.
Returns
- bool
Whether or not the vector and the object are equal.
Floor()
Returns a new vector with all components rounded down (towards negative infinity).
public readonly Vector3D Floor()Returns
- Vector3D
A vector with Floor(double) called on each component.
GetHashCode()
Serves as the hash function for Vector3D.
public override readonly int GetHashCode()Returns
- int
A hash code for this vector.
Inverse()
Returns the inverse of this vector. This is the same as new Vector3D(1 / v.X, 1 / v.Y, 1 / v.Z).
public readonly Vector3D Inverse()Returns
- Vector3D
The inverse of this vector.
IsEqualApprox(Vector3D)
Returns true if this vector and other are approximately equal,
by running IsEqualApprox(double, double) on each component.
public readonly bool IsEqualApprox(Vector3D other)Parameters
otherVector3DThe other vector to compare.
Returns
- bool
Whether or not the vectors are approximately equal.
IsFinite()
Returns true if this vector is finite, by calling IsFinite(double) on each component.
public readonly bool IsFinite()Returns
- bool
Whether this vector is finite or not.
IsNormalized()
public readonly bool IsNormalized()Returns
IsZeroApprox()
Returns true if this vector's values are approximately zero, by running IsZeroApprox(double) on each component. This method is faster than using IsEqualApprox(Vector3D) with one value as a zero vector.
public readonly bool IsZeroApprox()Returns
- bool
Whether or not the vector is approximately zero.
Length()
Returns the length (magnitude) of this vector.
public readonly double Length()Returns
- double
The length of this vector.
- See Also
LengthSquared()
Returns the squared length (squared magnitude) of this vector. This method runs faster than Length(), so prefer it if you need to compare vectors or need the squared length for some formula.
public readonly double LengthSquared()Returns
- double
The squared length of this vector.
Lerp(Vector3D, double)
Returns the result of the linear interpolation between
this vector and to by amount weight.
public readonly Vector3D Lerp(Vector3D to, double weight)Parameters
toVector3DThe destination vector for interpolation.
weightdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
Returns
- Vector3D
The resulting vector of the interpolation.
LimitLength(double)
Returns the vector with a maximum length by limiting its length to length.
public readonly Vector3D LimitLength(double length = 1)Parameters
lengthdoubleThe length to limit to.
Returns
- Vector3D
The vector with its length limited.
MaxAxisIndex()
Returns the axis of the vector's highest value. See Axis. If all components are equal, this method returns X.
public readonly Axis MaxAxisIndex()Returns
- Axis
The index of the highest axis.
MinAxisIndex()
Returns the axis of the vector's lowest value. See Axis. If all components are equal, this method returns Z.
public readonly Axis MinAxisIndex()Returns
- Axis
The index of the lowest axis.
MoveToward(Vector3D, double)
Moves this vector toward to by the fixed delta amount.
public readonly Vector3D MoveToward(Vector3D to, double delta)Parameters
Returns
- Vector3D
The resulting vector.
Normalized()
Returns the vector scaled to unit length. Equivalent to v / v.Length().
public readonly Vector3D Normalized()Returns
- Vector3D
A normalized version of the vector.
Project(Vector3D)
Returns this vector projected onto another vector onNormal.
public readonly Vector3D Project(Vector3D onNormal)Parameters
onNormalVector3DThe vector to project onto.
Returns
- Vector3D
The projected vector.
Reflect(Vector3D)
Returns this vector reflected from a plane defined by the given normal.
public readonly Vector3D Reflect(Vector3D normal)Parameters
normalVector3DThe normal vector defining the plane to reflect from. Must be normalized.
Returns
- Vector3D
The reflected vector.
Rotated(Vector3D, double)
Rotates this vector around a given axis vector by angle (in radians).
The axis vector must be a normalized vector. Warning: uses floating-point maths internally.
public readonly Vector3D Rotated(Vector3D axis, double angle)Parameters
axisVector3DThe vector to rotate around. Must be normalized.
angledoubleThe angle to rotate by, in radians.
Returns
- Vector3D
The rotated vector.
Round()
Returns this vector with all components rounded to the nearest integer, with halfway cases rounded towards the nearest multiple of two.
public readonly Vector3D Round()Returns
- Vector3D
The rounded vector.
Sign()
Returns a vector with each component set to one or negative one, depending on the signs of this vector's components, or zero if the component is zero, by calling Sign(double) on each component.
public readonly Vector3D Sign()Returns
- Vector3D
A vector with all components as either
1,-1, or0.
SignedAngleTo(Vector3D, Vector3D)
Returns the signed angle to the given vector, in radians.
The sign of the angle is positive in a counter-clockwise
direction and negative in a clockwise direction when viewed
from the side specified by the axis.
public readonly double SignedAngleTo(Vector3D to, Vector3D axis)Parameters
toVector3DThe other vector to compare this vector to.
axisVector3DThe reference axis to use for the angle sign.
Returns
- double
The signed angle between the two vectors, in radians.
Slerp(Vector3D, double)
Returns the result of the spherical linear interpolation between
this vector and to by amount weight.
This method also handles interpolating the lengths if the input vectors have different lengths. For the special case of one or both input vectors having zero length, this method behaves like Lerp(Vector3D, double).
public readonly Vector3D Slerp(Vector3D to, double weight)Parameters
toVector3DThe destination vector for interpolation.
weightdoubleA value on the range of 0.0 to 1.0, representing the amount of interpolation.
Returns
- Vector3D
The resulting vector of the interpolation.
Slide(Vector3D)
Returns this vector slid along a plane defined by the given normal.
public readonly Vector3D Slide(Vector3D normal)Parameters
normalVector3DThe normal vector defining the plane to slide on.
Returns
- Vector3D
The slid vector.
Snapped(Vector3D)
Returns this vector with each component snapped to the nearest multiple of step.
This can also be used to round to an arbitrary number of decimals.
public readonly Vector3D Snapped(Vector3D step)Parameters
stepVector3DA vector value representing the step size to snap to.
Returns
- Vector3D
The snapped vector.
ToString()
Converts this Vector3D to a string.
public override readonly string ToString()Returns
- string
A string representation of this vector.
ToString(string?)
Converts this Vector3D to a string with the given format.
public readonly string ToString(string? format)Parameters
formatstring
Returns
- string
A string representation of this vector.
Operators
operator +(Vector3D, Vector3D)
public static Vector3D operator +(Vector3D left, Vector3D right)Parameters
Returns
- Vector3D
The added vector.
operator /(Vector3D, Vector3D)
public static Vector3D operator /(Vector3D vec, Vector3D divisorv)Parameters
Returns
- Vector3D
The divided vector.
operator /(Vector3D, double)
public static Vector3D operator /(Vector3D vec, double divisor)Parameters
Returns
- Vector3D
The divided vector.
operator ==(Vector3D, Vector3D)
Returns true if the vectors are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Vector3D) instead, which is more reliable.
public static bool operator ==(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the vectors are exactly equal.
operator >(Vector3D, Vector3D)
Compares two Vector3D vectors by first checking if
the X value of the left vector is greater than
the X value of the right vector.
If the X values are exactly equal, then it repeats this check
with the Y values of the two vectors, and then with the Z values.
This operator is useful for sorting vectors.
public static bool operator >(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the left is greater than the right.
operator >=(Vector3D, Vector3D)
Compares two Vector3D vectors by first checking if
the X value of the left vector is greater than
or equal to the X value of the right vector.
If the X values are exactly equal, then it repeats this check
with the Y values of the two vectors, and then with the Z values.
This operator is useful for sorting vectors.
public static bool operator >=(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the left is greater than or equal to the right.
operator !=(Vector3D, Vector3D)
Returns true if the vectors are not equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Vector3D) instead, which is more reliable.
public static bool operator !=(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the vectors are not equal.
operator <(Vector3D, Vector3D)
Compares two Vector3D vectors by first checking if
the X value of the left vector is less than
the X value of the right vector.
If the X values are exactly equal, then it repeats this check
with the Y values of the two vectors, and then with the Z values.
This operator is useful for sorting vectors.
public static bool operator <(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the left is less than the right.
operator <=(Vector3D, Vector3D)
Compares two Vector3D vectors by first checking if
the X value of the left vector is less than
or equal to the X value of the right vector.
If the X values are exactly equal, then it repeats this check
with the Y values of the two vectors, and then with the Z values.
This operator is useful for sorting vectors.
public static bool operator <=(Vector3D left, Vector3D right)Parameters
Returns
- bool
Whether or not the left is less than or equal to the right.
operator %(Vector3D, Vector3D)
Gets the remainder of each component of the Vector3D with the components of the given Vector3D. This operation uses truncated division, which is often not desired as it does not work well with negative numbers.
public static Vector3D operator %(Vector3D vec, Vector3D divisorv)Parameters
Returns
- Vector3D
The remainder vector.
Examples
GD.Print(new Vector3D(10, -20, 30) % new Vector3D(7, 8, 9)); // Prints "(3, -4, 3)"operator %(Vector3D, double)
Gets the remainder of each component of the Vector3D with the components of the given double. This operation uses truncated division, which is often not desired as it does not work well with negative numbers.
public static Vector3D operator %(Vector3D vec, double divisor)Parameters
Returns
- Vector3D
The remainder vector.
Examples
GD.Print(new Vector3D(10, -20, 30) % 7); // Prints "(3, -6, 2)"operator *(Vector3D, Vector3D)
public static Vector3D operator *(Vector3D left, Vector3D right)Parameters
Returns
- Vector3D
The multiplied vector.
operator *(Vector3D, double)
public static Vector3D operator *(Vector3D vec, double scale)Parameters
Returns
- Vector3D
The multiplied vector.
operator *(double, Vector3D)
public static Vector3D operator *(double scale, Vector3D vec)Parameters
Returns
- Vector3D
The multiplied vector.
operator -(Vector3D, Vector3D)
public static Vector3D operator -(Vector3D left, Vector3D right)Parameters
Returns
- Vector3D
The subtracted vector.
operator -(Vector3D)
Returns the negative value of the Vector3D.
This is the same as writing new Vector3D(-v.X, -v.Y, -v.Z).
This operation flips the direction of the vector while
keeping the same magnitude.
With floats, the number zero can be either positive or negative.
public static Vector3D operator -(Vector3D vec)Parameters
vecVector3DThe vector to negate/flip.
Returns
- Vector3D
The negated/flipped vector.