Matrix translation

Author: k | 2025-04-25

Coordinate matrix, translation matrix. Reflection matrix, translation matrix. Translation matrix, coordinate matrix. Translation matrix, rotation matrix. There’s just one step to solve this. The inverse of a translation matrix is the translation matrix with the opposite signs on each of the translation components. The inverse of a rotation matrix is the rotation matrix's transpose. The

Scaling Matrix and Translation Matrix related issue

Struct in UnityEngine/Implemented in:UnityEngine.CoreModuleSuggest a changeSuccess!Thank you for helping us improve the quality of Unity Documentation. Although we cannot accept all submissions, we do read each suggested change from our users and will make updates where applicable.CloseSubmission failedFor some reason your suggested change could not be submitted. Please try again in a few minutes. And thank you for taking the time to help us improve the quality of Unity Documentation.CloseYour nameYour emailSuggestion*CancelDescriptionA standard 4x4 transformation matrix.A transformation matrix can perform arbitrary linear 3D transformations (i.e. translation, rotation, scale, shear etc.)and perspective transformations using homogenous coordinates. You rarely use matrices in scripts; mostoften using Vector3s, Quaternions and functionality of Transform class is more straightforward. Plain matrices are used in special caseslike setting up nonstandard camera projection.In Unity, several Transform, Camera, Material, Graphics and GL functions use Matrix4x4.Matrices in Unity are column major; i.e. the position of a transformation matrix is in the last column,and the first three columns contain x, y, and z-axes. Data is accessed as:row + (column*4). Matrices can beindexed like 2D arrays but note that in an expression like mat[a, b], a refers to the row index, while b refersto the column index.using UnityEngine;public class ExampleScript : MonoBehaviour{ void Start() { // get matrix from the Transform var matrix = transform.localToWorldMatrix; // get position from the last column var position = new Vector3(matrix[0,3], matrix[1,3], matrix[2,3]); Debug.Log("Transform position from matrix is: " + position); }}Static PropertiesidentityReturns the identity matrix (Read Only).zeroReturns a matrix with all elements set to zero (Read Only).PropertiesdecomposeProjectionThis property takes a projection matrix and returns the six plane coordinates that define a projection frustum.determinantThe determinant of the matrix. (Read Only)inverseThe inverse of this matrix. (Read Only)isIdentityChecks whether this is an identity matrix. (Read Only)lossyScaleAttempts to get a scale value from the matrix. (Read Only)rotationAttempts to get a rotation quaternion from this matrix.this[int,int]Access element at [row, column].transposeReturns the transpose of this matrix (Read Only).Public MethodsGetColumnGet a column of the matrix.GetRowReturns a row of the matrix.MultiplyPointTransforms a position by this matrix (generic).MultiplyPoint3x4Transforms a position by this matrix (fast).MultiplyVectorTransforms a direction by this matrix.SetColumnSets a column of the matrix.SetRowSets a row of the matrix.SetTRSSets this matrix to a translation, rotation and scaling matrix.ToStringReturns a formatted string for this matrix.TransformPlaneReturns a plane that is transformed in space.ValidTRSChecks if this matrix is a valid transform matrix.Static MethodsFrustumThis function returns a projection matrix with viewing frustum that has a near plane defined by the coordinates that were passed in.Inverse3DAffineComputes the inverse of a 3D affine matrix.LookAtCreate a "look at" matrix.OrthoCreate an orthogonal projection matrix.PerspectiveCreate a perspective projection matrix.RotateCreates a rotation matrix.ScaleCreates a scaling matrix.TranslateCreates a translation matrix.TRSCreates a translation, rotation and scaling matrix.OperatorsDid you find this page useful? Please give it a rating: Function on a node. The nodeToSnap parameter is optional. If it's not specified, or is None, we use the result of nuke.thisNode() instead. The node must have an Enumeration_Knob called "snapFunc" which selects the snapping function to call. ''' if nodeToSnap is None: nodeToSnap = nuke.thisNode() # Make sure that the nodeToSnap has a snapFunc knob if "snapFunc" not in nodeToSnap.knobs(): # TODO: warn the user that we can't snap this node. return snapFunc = dict(snapFuncs)[nodeToSnap['snapFunc'].value()] snapFunc(nodeToSnap)[docs]def radians(vector) -> list: return [math.radians(x) for x in vector][docs]def degrees(vector) -> list: return [math.degrees(x) for x in vector][docs]def scalingMatrix(scalings) -> _nukemath.Matrix4: ''' Generates a scaling matrix from the input vector. @type scalings: _nukemath.Vector3 @param scalings: Vector that will be used generate the scaling matrix. @return: The scaling matrix. ''' m = _nukemath.Matrix4() m.makeIdentity() m.scaling(scalings[0], scalings[1], scalings[2]) return m[docs]def translateMatrix(translations) -> _nukemath.Matrix4: ''' Generates a translation matrix from the input vector. @type translations: _nukemath.Vector3 @param translations: Vector that will be used generate the translation matrix. @return: The translate matrix. ''' m = _nukemath.Matrix4() m.makeIdentity() m.translation(translations[0], translations[1], translations[2]) return m[docs]def rotateMatrixXYZ(rotations) -> _nukemath.Matrix4: ''' Generates a rotation XYZ matrix from the input vector. @type rotations: _nukemath.Vector3 @param rotations: Vector that will be used generate the rotate matrix. @return: The rotate matrix. ''' m = _nukemath.Matrix4() m.makeIdentity() m.rotateZ(rotations[2]) m.rotateY(rotations[1]) m.rotateX(rotations[0]) return m[docs]def rotateMatrixZXY(rotations) -> _nukemath.Matrix4: ''' Generates a rotation ZXY matrix from the input vector. @type rotations: _nukemath.Vector3 @param rotations: Vector that will be used generate the rotate matrix. @return: The rotate matrix. ''' m = _nukemath.Matrix4() m.makeIdentity() m.rotateY(rotations[1]) m.rotateX(rotations[0]) m.rotateZ(rotations[2]) return m[docs]def transformMatrix(nodeToSnap) -> _nukemath.Matrix4: ''' Generates the transformation matrix for a given node based on its knob values. @type nodeToSnap: nuke.Node @param nodeToSnap: Node from which the data will be extracted to generate its transformation matrix. @return: The matrix containg all node transformations. ''' T = translateMatrix(nodeToSnap['translate'].getValue()) R = rotateMatrixZXY(radians(nodeToSnap['rotate'].getValue())) S = scalingMatrix(nodeToSnap['scaling'].getValue()) pT = translateMatrix(nodeToSnap['pivot_translate'].getValue()) pR = rotateMatrixXYZ(radians(nodeToSnap['pivot_rotate'].getValue())) pTi = pT.inverse() pRi = pR.inverse() return pT * pR * T * R * S * pRi * pTi[docs]def translateRotatePivot(nodeToSnap, translate, rotate) -> tuple: ''' Pivot translation and rotation must keep the object stationary and in order to do that compensation values must be placed in the geometry translate and rotate. @type nodeToSnap: nuke.Node @param nodeToSnap: Node to translate and rotate @type translate: _nukemath.Vector3 @param translate: Target position for the pivot point. @type rotate: _nukemath.Vector3 @param rotate: Target rotation for the pivot point. @return: A tuple with the new geometry translation and rotation respectively (_nukemath.Vector3, _nukemath.Vector3). ''' pT = translateMatrix(translate) pTi = pT.inverse() pR = rotateMatrixXYZ(rotate) pRi = pR.inverse() S = scalingMatrix(nodeToSnap['scaling'].getValue()) Si = S.inverse() M = transformMatrix(nodeToSnap) compensatedM = pRi * pTi * M * pT * pR * Si geoTranslate = compensatedM.translation() geoRotate = degrees(compensatedM.rotationsZXY()) return (geoTranslate, geoRotate)

Translating objects with a Transformation Matrix

I posted this question and found some theory on matrix calculations, but this is way over my head in the math and excel department. Your spreadsheet works perfectly for my intended purpose. I have checked it a few times utilizing CAD. I see your 2nd post indicating "the last column of the transform matrix should be zero but for the last". It seems the spreadsheet works with that column with all 1's or 3 0's and a 1. Thank you again so much for freely sharing your brilliance. I'd hope somehow that I could return the favor, it not to you, then to someone else. 06-03-2013, 08:42 PM #5 Re: 3D Coordinate Translation and Rotation Formulas for Excel. You're welcome. It seems the spreadsheet works with that column with all 1's or 3 0's and a 1. It's doesn't matter for this case, but it makes the homogeneous coordinate W=1, which is essential if additional transformations are to be applied to the result. 09-30-2014, 03:40 PM #6 Registered User Re: 3D Coordinate Translation and Rotation Formulas for Excel. I am trying to get Excel to do something very similar to the OP - so I believe this posted solution may work for me. When I look at the file, however, it appears that the inputs to the transformation are the trans x,y,z and the roll,pitch,yaw angles. What I am looking for is to have Excel calculate the 4x4 matrix (rotation with translation), derived from the A,B,C and A',B',C' points. I don't know my translation and roll,pitch,yaw (and don't really care) - I just want to be able to pass additional points (D,E, etc) through the same transform to get D',E', etc.Can this file be modified to suit my needs, or does somebody have a better solution? Thanks! 10-01-2014, 10:37 AM #7 Re: 3D Coordinate Translation and Rotation Formulas for Excel. The posted solution turned out to be insufficient. Here was the problem.Given two congruent triangles in space ({A1,B1,C1} and {A2,B2,C2}), find the homogeneous transform matrix that maps one to the other.The solution was to 1) Form a homogeneous translation matrix that puts A1 at the origin,2) Form a quaternion rotation that puts B1 along +z (it can't be a Euler angle rotation, because that could gimbal lock). Convert the quaternion to a homogeneous rotation matrix. 3) Form a rotation about +z to put C1 in the x-y plane4, 5, 6) Repeat steps 1 to 3 for the second triangleThe matrix derived in steps 1 to 3, times the inverse of the matrix in steps 4 to 6, maps triangle 1 to triangle 2.Easy for a mathematician, but a struggle for this engineer. Last edited by shg; 10-01-2014 at 11:10 AM.. Coordinate matrix, translation matrix. Reflection matrix, translation matrix. Translation matrix, coordinate matrix. Translation matrix, rotation matrix. There’s just one step to solve this.

models.translation_matrix – Translation Matrix modelgensim

Deprecated in Current ReleaseRequirementsSoftware operationDefining Calibration TasksDefinitions and TheorySupported SystemsSupported TargetsRequired EvidenceTest SetupCalibration ProcedureUser InterfaceUse in Imatest ITModule settingsModule outputsDefining a DeviceDefining DistortionDefining the System of DevicesDefining the TargetDefining a Test CaptureDefining a Test ImageHomogenous CoordinatesProjective Camera ModelMulti-Camera SystemsDistortion ModelsCoordinate SystemsRotations and TranslationsTranslationsLet \(\mathbf{X}=\left[\begin{array}{ccc}X&Y&Z\end{array}\right]^{\top}\) be a point in \(\mathbb{R}^3\) and let \(\mathbf{X}’=\left[\begin{array}{ccc}X’&Y’&Z’\end{array}\right]^{\top}\) be \(\mathbf{X}\) after a translation by \(\left[\begin{array}{ccc}\Delta X&\Delta Y&\Delta Z\end{array}\right]^{\top}\). Translations may be represented by a single \(4\times4\) matrix acting on a \(4\times1\) homogeneous coordinate. \(\begin{bmatrix}X’\\Y’\\Z’\\1\end{bmatrix}=\begin{bmatrix}1&0&0&\Delta X\\0&1&0&\Delta Y\\0&0&1&\Delta Z\\0&0&0&1\end{bmatrix}\begin{bmatrix}X\\Y\\Z\\1\end{bmatrix}=\begin{bmatrix}X+\Delta X\\Y+\Delta Y\\Z+\Delta Z\\1\end{bmatrix}\)A translation can be inverted by applying the negative of the translation terms\(\begin{bmatrix}X\\Y\\Z\\1\end{bmatrix}=\begin{bmatrix}1&0&0&\Delta X\\0&1&0&\Delta Y\\0&0&1&\Delta Z\\0&0&0&1\end{bmatrix}^{-1}\begin{bmatrix}X’\\Y’\\Z’\\1\end{bmatrix}=\begin{bmatrix}1&0&0&-\Delta X\\0&1&0&-\Delta Y\\0&0&1&-\Delta Z\\0&0&0&1\end{bmatrix}\begin{bmatrix}X’\\Y’\\Z’\\1\end{bmatrix}\)RotationsIn \(\mathbb{R}^3\), the rotation of points about the origin are described by a \(3\times3\) matrix \(\mathbf{R}\). Valid rotation matrices obey the following properties:\(\mathrm{det}\left(\mathbf{R}\right) = +1\)\(\mathbf{R}^{-1}=\mathbf{R}^{\top}\)From these properties, both the columns and rows of \(\mathbf{R}\) are orthonormal.The rotation is applied by left-multipling the points by the rotation matrix.\(\begin{bmatrix}X’\\Y’\\Z’\end{bmatrix}=\begin{bmatrix}R_{11}&R_{12}&R_{13}\\R_{21}&R_{22}&R_{23}\\R_{31}&R_{32}&R_{33}\end{bmatrix}\begin{bmatrix}X\\Y\\Z\end{bmatrix}=\begin{bmatrix}R_{11}X+R_{12}Y+R_{13}Z\\R_{21}X+R_{22}Y+R_{23}Z\\R_{31}X+R_{32}Y+R_{33}Z\end{bmatrix}\)Rotations of 3D homogeneous may be defined by a \(4\times4\) matrix\(\begin{bmatrix}X’\\Y’\\Z’\\1\end{bmatrix}=\begin{bmatrix}R_{11}&R_{12}&R_{13}&0\\R_{21}&R_{22}&R_{23}&0\\R_{31}&R_{32}&R_{33}&0\\0&0&0&1\end{bmatrix}\begin{bmatrix}X\\Y\\Z\\1\end{bmatrix}\)Rotation of axes are defined by the inverse (transpose) of the rotation matrix transforming points by the same amount. A rotation of axes is also referred to as a pose. Unless specified, the rest of this page uses implies rotation to be a rotation of points about the origin.Basic RotationsA non-rotation is described by an identity matrix\(\mathbf{R}_{0}(\theta)=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\)The right-handed rotation of points about the the \(X\), \(Y\), and \(Z\) axes are given by:\(\mathbf{R}_{X}(\theta)=\begin{bmatrix}1&0&0\\0&\cos\theta&-\sin\theta\\0&\sin\theta&\cos\theta\end{bmatrix}\)\(\mathbf{R}_{Y}(\theta)=\begin{bmatrix}\cos\theta&0&\sin\theta\\0&1&0\\-\sin\theta&0&\cos\theta\end{bmatrix}\)\(\mathbf{R}_{Z}(\theta)=\begin{bmatrix}\cos\theta&-\sin\theta&0\\\sin\theta&\cos\theta&0\\0&0&1\end{bmatrix}\)The inverse of these rotations are given by:\(\mathbf{R}^{-1}_{X}(\theta)=\mathbf{R}_{X}(-\theta)=\begin{bmatrix}1&0&0\\0&\cos\theta&\sin\theta\\0&-\sin\theta&\cos\theta\end{bmatrix}\)\(\mathbf{R}^{-1}_{Y}(\theta)=\mathbf{R}_{Y}(-\theta)=\begin{bmatrix}\cos\theta&0&-\sin\theta\\0&1&0\\\sin\theta&0&\cos\theta\end{bmatrix}\)\(\mathbf{R}^{-1}_{Z}(\theta)=\mathbf{R}_{Z}(-\theta)=\begin{bmatrix}\cos\theta&\sin\theta&0\\-\sin\theta&\cos\theta&0\\0&0&1\end{bmatrix}\)The rotation of axes by \(\theta\) radians is equivalent to a rotation of points by \(-\theta\) radians. The choices of rotation of bases or rotation of points and handedness of the rotation(s) should be specified to all relevant parties to avoid ambiguities in meaning. Chaining RotationsRotations may be combined in sequence by matrix-multiplying their rotation matrices. When performing sequences of rotations, later rotations are left-multiplied. For example a transform is defined by first rotating by \(\mathbf{R}_1\), then by \(\mathbf{R}_2\), and finally by \(\mathbf{R}_3\), the single rotation \(\mathbf{R}\) that describes the sequence of rotations is\(\mathbf{R}=\mathbf{R}_3\mathbf{R}_2\mathbf{R}_1\)Rotation-Translation CombinationsRotation-Translation MatricesA rotation about the origin followed by a translation may be described by a single \(4\times4\) matrix\(\begin{bmatrix}\mathbf{R}&\mathbf{t}\\\mathbf{0}^{\top}&1\end{bmatrix}\)where \(\mathbf{R}\) is the \(3\times3\) rotation matrix, \(\mathbf{t}\) is the \(3\times1\) translation, and \(\mathbf{0}\) is the \(3\times1\) vector of zeros.Since the last row of the \(4\times4\) rotation-translation matrix is always \(\begin{bmatrix}0&0&0&1\end{bmatrix}\), they are sometimes shorthanded to a \(3\times4\) augmented matrix\(\left[\begin{array}{c|c}\mathbf{R}&\mathbf{t}\end{array}\right]=\left[\begin{array}{ccc|c}R_{11}&R_{12}&R_{13}&t_{1}\\R_{21}&R_{22}&R_{23}&t_{2}\\R_{31}&R_{32}&R_{33}&t_{3}\end{array}\right]\)Note that when using this shorthand, matrix math is technically being broken as you cannot matrix multiply a \(3\times4\) matrix with a \(3\times4\) matrix. It is the implicit last row that is always the same that allows us to get away with this shorthand.Rotation-Translation InverseThe inverse of a rotation-translation matrix is given by\(\left[\begin{array}{c|c}\mathbf{R}&\mathbf{t}\end{array}\right]^{-1}=\left[\begin{array}{c|c}\mathbf{R}^{-1}&-\mathbf{R}^{-1}\mathbf{t}\end{array}\right]=\left[\begin{array}{c|c}\mathbf{R}^{\top}&-\mathbf{R}^{\top}\mathbf{t}\end{array}\right]\)Chaining Rotation-TranslationsJust like pure rotation matrices, later rotation-translation transforms are left multiplied. Given Matrix Applications: Matrices in GraphicsIntroductionIn the world of computer graphics, matrices play a crucial role in transforming and manipulating objects on the screen. Whether it's rotating a 3D model, scaling an image, or applying a perspective transformation, matrices provide the mathematical foundation for these operations. In this tutorial, we will dive deep into the world of matrices and explore their applications in graphics.What is a Matrix?A matrix is a rectangular array of numbers arranged in rows and columns. It is often used to represent linear transformations and perform mathematical operations. In graphics, matrices are primarily used to represent transformations such as translation, rotation, scaling, and shearing.Matrix OperationsMatrix Addition and SubtractionMatrix addition and subtraction are straightforward operations that involve adding or subtracting corresponding elements of two matrices. Let's take a look at an example:# Matrix additionA = [[1, 2], [3, 4]]B = [[5, 6], [7, 8]]C = [[0, 0], [0, 0]]for i in range(len(A)): for j in range(len(A[0])): C[i][j] = A[i][j] + B[i][j]print(C)Output:[[6, 8], [10, 12]]Matrix MultiplicationMatrix multiplication is a fundamental operation in graphics. It involves multiplying corresponding elements of rows and columns to obtain the resulting matrix. Here's an example:# Matrix multiplicationA = [[1, 2], [3, 4]]B = [[5, 6], [7, 8]]C = [[0, 0], [0, 0]]for i in range(len(A)): for j in range(len(B[0])): for k in range(len(B)): C[i][j] += A[i][k] * B[k][j]print(C)Output:[[19, 22], [43, 50]]Matrix TranspositionMatrix transposition involves interchanging rows and columns of a matrix. It can be achieved by simply swapping the elements across the main diagonal. Here's an example:# Matrix transpositionA = [[1, 2, 3], [4, 5, 6]]B = [[0, 0], [0, 0], [0, 0]]for i in range(len(A)): for j in range(len(A[0])): B[j][i] = A[i][j]print(B)Output:[[1, 4], [2, 5], [3, 6]]Matrices in GraphicsNow that we have covered the basic matrix operations, let's explore how matrices are used in graphics. Matrices are primarily used to represent transformations such as translation, rotation, scaling, and shearing.TranslationTranslation involves moving an object from one position to another. It can be achieved by adding a translation matrix to the original coordinates of the object. Here's an example:# Translation matrixT = [[1, 0, dx], [0, 1, dy], [0, 0, 1]]# Original coordinatesP = [x, y, 1]# Translated coordinatesP' = T * PRotationRotation involves rotating an object around a specified point or axis. It can be achieved by multiplying the original coordinates of the object by a rotation matrix. Here's an example:# Rotation matrix (counter-clockwise)R = [[cos(theta), -sin(theta), 0], [sin(theta), cos(theta), 0], [0, 0, 1]]# Original coordinatesP = [x, y, 1]# Rotated coordinatesP' = R * PScalingScaling involves resizing an object by multiplying its coordinates by a scaling matrix. It can be used to make an object larger or smaller. Here's an example:# Scaling matrixS = [[sx, 0, 0], [0, sy, 0], [0, 0, 1]]# Original coordinatesP = [x, y, 1]# Scaled coordinatesP' = S * PShearingShearing involves distorting an object along a specified axis. It can be achieved by multiplying the original coordinates of the object by a shearing matrix. Here's an example:# Shearing matrixH

Free Matrix Calculator. Calculate Matrix Online - Binary Translator

Right direction vector from the matrixLeft: The left direction vector from the matrixForward: The forward direction vector in right-handed (RH) coordinates from the matrixBackward: The backward direction vector in right-handed (RH) coordinates from the matrixTranslation: Returns the translation in the matrixMethodsComparison operators: == and !=Assignment operators: =, +=, -=, *=, /=Unary operators: +, -Binary operators: +, -, *, /Decompose: Decomposes the matrix into rotation (a Quaternion), scaling, and translation components. Returns false if the matrix can't be decomposed.Transpose: Computes the transpose of the matrix. Note that for a pure rotation matrix, this is the same as the inverse.Invert: Computes the inverse of the matrix using Cramer's rule. It returns false if the matrix is not invertible.Determinant: Computes the determinant of the matrix.ToEuler: Computes rotation about y-axis (y), then x-axis (x), then z-axis (z) as angles in radians. The return value is compatible with one of the overloads of CreateFromYawPitchRoll. This result is only valid if the input matrix's upper 3x3 contains only rotation (i.e. no scaling).StaticsCreateBillboard: Creates a spherical billboard that rotates around a specified object positionCreateConstrainedBillboard: Creates a cylindrical billboard that rotates around a specified axisCreateTranslation: Creates a matrix for translating by the given X, Y, Z offset. Note you can create the inverse of this matrix by passing -X, -Y, -Z.CreateScale: Creates a matrix for scaling by the given X, Y, and Z scale factors. Note you can create the inverse of this matrix by passing 1/X, 1/Y, 1/Z.CreateRotationX, CreateRotationY, CreateRotationZ: Creates a matrix for rotation about the

Translation and rotation in one matrix - LaValle

Verbose levelcore.removeConsoleVerbose(level)ParametersNameTypeDefaultDescriptionlevelVerboseVerbose levelremoveLogFileVerboseRemove a log file verbose levelcore.removeLogFileVerbose(level)ParametersNameTypeDefaultDescriptionlevelVerboseVerbose levelremoveSessionLogFileVerboseRemove a session log file (lastSession.log) verbose levelcore.removeSessionLogFileVerbose(level)ParametersNameTypeDefaultDescriptionlevelVerboseVerbose levelsetLogFileSet the path of the log fileParametersNameTypeDefaultDescriptionpathOutputFilePathPath of the log fileGeomapplyTransformApply a transformation matrix to a geometrical entitygeom.applyTransform(entity, [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]])ParametersNameTypeDefaultDescriptionentityGeomEntityThe geometric entitymatrixMatrix4[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]The transformation matrixgetEntityAABBRetrieve the Axis-Aligned Bounded Box of a geometric entitygeom.getEntityAABB(entity)ParametersNameTypeDefaultDescriptionentityGeomEntityThe geometric entityReturnsNameTypeDescriptionaabbAABBThe axis aligned bounded boxchangeOfBasisMatrixConstruct a Change of Basis Matrix (e.g multiplying the point [0,0,0] will result to the point origin)geom.changeOfBasisMatrix(origin, x, y, z)ParametersNameTypeDefaultDescriptionoriginPoint3Origin of the new basisxVector3X axis of the new basisyVector3Y axis of the new basiszVector3Z axis of the new basisReturnsNameTypeDescriptionchangeOfBasisMatrix4The change of basis matrixfromLookAtMatrixGet camera position, up and target vectorsgeom.fromLookAtMatrix(matrix, 1)ParametersNameTypeDefaultDescriptionmatrixMatrix4The created MatrixdistanceFromTargetDistance1ReturnsNameTypeDescriptionpositionPoint3The camera positionupVector3The up vectortargetPoint3The target positionfromOriginNormalCreate a Matrix from an origin and a normal vectorgeom.fromOriginNormal(origin, normal)ParametersNameTypeDefaultDescriptionoriginPoint3The origin pointnormalVector3The normal vectorReturnsNameTypeDescriptionmatrixMatrix4The created MatrixfromTRSCreate a Matrix from translation, rotation and scaling vectorsParametersNameTypeDefaultDescriptionTVector3The translation vectorRVector3The rotations vectorSVector3The scaling vectorReturnsNameTypeDescriptionmatrixMatrix4The created MatrixinvertMatrixInvert a matrixgeom.invertMatrix(geom.IdentityMatrix4)ParametersNameTypeDefaultDescriptionmatrixMatrix4geom.IdentityMatrix4The matrix to invertReturnsNameTypeDescriptioninvertedMatrix4The inverted matrixlookAtMatrixCreate a matrix from a camera position, up and targetgeom.lookAtMatrix(position, up, target)ParametersNameTypeDefaultDescriptionpositionPoint3The camera positionupVector3The up vectortargetPoint3The target positionReturnsNameTypeDescriptionmatrixMatrix4The created matrixmultiplyMatricesMultiply two matrices, returns left*rightgeom.multiplyMatrices(geom.IdentityMatrix4, geom.IdentityMatrix4)ParametersNameTypeDefaultDescriptionleftMatrix4geom.IdentityMatrix4Left side matrixrightMatrix4geom.IdentityMatrix4Right side matrixReturnsNameTypeDescriptionresultMatrix4Result of the matrices multiplicationmultiplyMatrixPointMultiply a point by a matrix (i.e apply the matrix to a point)geom.multiplyMatrixPoint(geom.IdentityMatrix4, point)ParametersNameTypeDefaultDescriptionmatrixMatrix4geom.IdentityMatrix4The matrix to applypointPoint3The point to multiplyReturnsNameTypeDescriptionresultPoint3The resulting pointmultiplyMatrixVectorMultiply a vector by a matrix (i.e apply the matrix to a vector)geom.multiplyMatrixVector(geom.IdentityMatrix4, vector)ParametersNameTypeDefaultDescriptionmatrixMatrix4geom.IdentityMatrix4The matrix to applyvectorVector3The vector to multiplyReturnsNameTypeDescriptionresultVector3The resulting pointorthographicMatrixCreate an orthographic matrix from a 3D width, a 3D height, a near, and a far clipping distancegeom.orthographicMatrix(width3D, height3D, nearClipDistance, farClipDistance)ParametersNameTypeDefaultDescriptionwidth3DDoubleThe 3D width to considerheight3DDoubleThe 3D height to considernearClipDistanceDistanceThe near clipping distancefarClipDistanceDistanceThe far clipping distanceReturnsNameTypeDescriptionmatrixMatrix4The created matrixperspectiveMatrixCreate a perspective matrix from a fovX, an aspect ratio, a near, and a far clipping distancegeom.perspectiveMatrix(fovX, aspectRatio, nearClipDistance, farClipDistance)ParametersNameTypeDefaultDescriptionfovXDoubleThe field of view on the x axis (degrees)aspectRatioDoubleThe aspect ratio foxX/fovYnearClipDistanceDistanceThe near clipping distancefarClipDistanceDistanceThe far clipping distanceReturnsNameTypeDescriptionmatrixMatrix4The created matrixtoTRSDecompose a Matrix into translation, rotation and scaling vectorsgeom.toTRS(geom.IdentityMatrix4)ParametersNameTypeDefaultDescriptionmatrixMatrix4geom.IdentityMatrix4The Matrix to be decomposedReturnsNameTypeDescriptionTRSVector3ListThe TRS listIOexportSceneToReflectExport current scene to a reflect projectio.exportSceneToReflect(0, "", "", False, "", True)ParametersNameTypeDefaultDescriptionrootOccurrence0Identifier of the destination occurrencesourceNameString""Push source nameuidString""UID of the push, overwrite old push if it's same UIDkeepHierarchyBooleanfalseKeep hierarchy or rake treeconfigFileFilePath""Use existing JSON config file, discard reflect UI promptdisableDecimationBooleantrueForces to disable the decimation applied on SyncObjectInstances on Reflect Server sideexportSceneExport a fileio.exportScene(fileName, 0)ParametersNameTypeDefaultDescriptionfileNameOutputFilePathPath of the file to exportrootOccurrence0Identifier of the root occurrence to exportexportSelectionExport the selection to a fileio.exportSelection(fileName, False)ParametersNameTypeDefaultDescriptionfileNameOutputFilePathPath of the file to exportkeepIntermediaryNodesBooleanfalseIf true, intermerdiary hierarchy is keptgetExportFormatsGive all the format name and their extensions that can be exported in PixyzReturnsNameTypeDescriptionformatsFormatListFormats that can be exported in PixyzgetImportFormatsGive all the format name and their extensions that can be imported in PixyzReturnsNameTypeDescriptionformatsFormatListFormats that can be imported in PixyzimportFilesImport filesio.importFiles(fileNames, 0)ParametersNameTypeDefaultDescriptionfileNamesFilesListList of files's paths to importrootOccurrence0Identifier of the destination occurrenceReturnsNameTypeDescriptiondestOccurrenceListThe root occurrences of each imported fileimportPictureImports a picture and applies. Coordinate matrix, translation matrix. Reflection matrix, translation matrix. Translation matrix, coordinate matrix. Translation matrix, rotation matrix. There’s just one step to solve this.

EBN: Chapter 3 – Translation Matrix

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