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## rotating a point on a 3D Plane... help!

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### #1Protricity  Members

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Posted 03 October 2001 - 09:05 AM

Im doing my first 3D game now, so I dont know how to calculate rotation yet. I know how to do rotation on a 2D plane, thats easy. So, basically, I have a point (ex. (1.0f,2.0f,1.5f) ) and I need to rotate it according to 3 Vector angles. ( ex. Xrotate = 45.0f, Yrotate = 35.0f, Zrotate = 25.0f) (0.0f,0.0f,0.0f) is the origin I need to rotate around. so, I need to make an algorithm for some method along the lines of Rotate( &X, &Y, &Z, Xrot, Yrot, Zrot) // (All are floats.) { } like I said, X,Y,Z is the point coordinates, and Xrot, Yrot, Zrot are the angles (from 0.0f to 360.0f) Using this information, how to I come up with a function that takes in the information and outputs the new point which has been rotated? I dont know if this is an advanced question, or its common knowledge, but if anyone can help me solve it Id very much apreciate it! thx, Protricity

### #2Dark  Members

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Posted 04 October 2001 - 12:06 AM

Hi

Well... I will just give you the basic operations.

//---------------------------------------------------------------------------------------------// Copyright © 2001 by Nucleus Software, Inc.// All rights reserved.//// $File:: CVector3D.H//$Dependencies:: none// $Revision:: 1//$Author:: Ebor Folkertsma// $Date:: 07-15-2001 8:42pm////$Description:: The CVector3D class offers some nice functionality for 3D vectors//---------------------------------------------------------------------------------------------#if _MSC_VER >= 1000 #pragma once#endif#ifndef _CVector3D_H_#define _CVector3D_H_#include class CVector3D;typedef CVector3D *LPCVector3D;class CVector3D{public: __inline CVector3D() {} __inline ~CVector3D() {} //--------------------------------------------------------------------------------------------- // CVector3D(const CVector3D& cVector3D) // // This is the initialize constructor, it enables you to specify startup values for the vector //--------------------------------------------------------------------------------------------- __inline CVector3D(const CVector3D& cVector3D) { fX = cVector3D.fX; fY = cVector3D.fY; fZ = cVector3D.fZ; } //--------------------------------------------------------------------------------------------- // CVector3D(const float& fNewX, const float& fNewY, const float& fNewZ) // // This is the initialize constructor, it enables you to specify startup values for the vector //--------------------------------------------------------------------------------------------- __inline CVector3D(const float &fNewX, const float &fNewY, const float &fNewZ) { fX = fNewX; fY = fNewY; fZ = fNewZ; } //--------------------------------------------------------------------------------------------- // CVector3D operator !(const CVector3D& cVector3D) const // // Reverses the vector //--------------------------------------------------------------------------------------------- __inline CVector3D operator !() const { return (*this * -1.0f); } //--------------------------------------------------------------------------------------------- // bool operator != (const CVector3D& cVector3D) const // // This function tests wheter two CVector3D classes are different //--------------------------------------------------------------------------------------------- __inline bool operator != (const CVector3D& cVector3D) const { if((fX == cVector3D.fX) && (fY == cVector3D.fY) && (fZ == cVector3D.fZ)) { return false; } return true; } //--------------------------------------------------------------------------------------------- // CVector3D operator * (const float& fValue) const // // This function multiplies the calling vector''s components by the give value //--------------------------------------------------------------------------------------------- __inline CVector3D operator * (const float& fValue) const { return CVector3D(fX * fValue, fY * fValue, fZ * fValue); } //--------------------------------------------------------------------------------------------- // void operator *= (const float& fValue) // // This function multiplies the vector''s components by the give value //--------------------------------------------------------------------------------------------- __inline void operator *= (const float& fValue) { fX *= fValue; fY *= fValue; fZ *= fValue; } //--------------------------------------------------------------------------------------------- // CVector3D operator + (const CVector3D& cVector3D) const // // This function adds this vector and the parameter vector and returns the result //--------------------------------------------------------------------------------------------- __inline CVector3D operator + (const CVector3D& cVector3D) const { return CVector3D(fX + cVector3D.fX, fY + cVector3D.fY, fZ + cVector3D.fZ); } //--------------------------------------------------------------------------------------------- // void operator += (const CVector3D& cVector3D) // // This function adds this vector and the parameter vector and sets the calling vector''s value // to the sum //--------------------------------------------------------------------------------------------- __inline void operator += (const CVector3D& cVector3D) { fX += cVector3D.fX; fY += cVector3D.fY; fZ += cVector3D.fZ; } //--------------------------------------------------------------------------------------------- // CVector3D operator - (const CVector3D& cVector3D) const // // This function substract the parameter vector from this vector and returns the result //--------------------------------------------------------------------------------------------- __inline CVector3D operator - (const CVector3D& cVector3D) const { return CVector3D(fX - cVector3D.fX, fY - cVector3D.fY, fZ - cVector3D.fZ); } //--------------------------------------------------------------------------------------------- // void operator -= (const CVector3D& cVector3D) // // This function substract the parameter vector from this vector and sets the calling vector''s // value to the result //--------------------------------------------------------------------------------------------- __inline void operator -= (const CVector3D& cVector3D) { fX -= cVector3D.fX; fY -= cVector3D.fY; fZ -= cVector3D.fZ; } //--------------------------------------------------------------------------------------------- // CVector3D operator / (const float& fValue) const // // This function divides the calling vector''s components by the give value //--------------------------------------------------------------------------------------------- __inline CVector3D operator / (const float& fValue) const { return CVector3D(fX / fValue, fY / fValue, fZ / fValue); } //--------------------------------------------------------------------------------------------- // void operator /= (const float& fValue) // // This function divides the vector''s components by the give value //--------------------------------------------------------------------------------------------- __inline void operator /= (const float& fValue) { fX /= fValue; fY /= fValue; fZ /= fValue; } //--------------------------------------------------------------------------------------------- // void operator = (const CVector3D& cVector3D) // // This function copies the properties from the parameter''s CVector3D class to the function // calling class //--------------------------------------------------------------------------------------------- __inline void operator = (const CVector3D& cVector3D) { fX = cVector3D.fX; fY = cVector3D.fY; fZ = cVector3D.fZ; } //--------------------------------------------------------------------------------------------- // bool operator == (const CVector3D& cVector3D) const // // This function tests wheter two CVector3D classes are equal //--------------------------------------------------------------------------------------------- __inline bool operator == (const CVector3D& cVector3D) const { if((fX == cVector3D.fX) && (fY == cVector3D.fY) && (fZ == cVector3D.fZ)) { return true; } return false; } //--------------------------------------------------------------------------------------------- // static float Angle(const CVector3D& cVector3D1, const CVector3D& cVector3D2) // // Returns the angle between the two vectors // Note that the parameter vectors must be NORMALIZED vectors!! //--------------------------------------------------------------------------------------------- __inline static float Angle(const CVector3D& cVector3D1, const CVector3D& cVector3D2) { return acosf(DotProduct(cVector3D1, cVector3D2)); } //--------------------------------------------------------------------------------------------- // float Angle(const CVector3D& cVector3D) // // Returns the angle between THIS vector and the cVector3D vector // Note that the THIS vector AND the parameter vector must be NORMALIZED vectors!! //--------------------------------------------------------------------------------------------- __inline float Angle(const CVector3D& cVector3D) { return acosf(DotProduct(*this, cVector3D)); } //--------------------------------------------------------------------------------------------- // static CVector3D CrossProduct(const CVector3D& cVector3D1, const CVector3D& cVector3D2) // // Calculate the cross-product of the two vectors and return the result vector //--------------------------------------------------------------------------------------------- __inline static CVector3D CrossProduct(const CVector3D &cVector3D1, const CVector3D &cVector3D2) { return CVector3D(cVector3D1.fY * cVector3D2.fZ - cVector3D1.fZ * cVector3D2.fY, cVector3D1.fZ * cVector3D2.fX - cVector3D1.fX * cVector3D2.fZ, cVector3D1.fX * cVector3D2.fY - cVector3D1.fY * cVector3D2.fX); } //--------------------------------------------------------------------------------------------- // static float DotProduct(const CVector3D &cVector3D) // // Calculate the dotproduct of the vector with itself //--------------------------------------------------------------------------------------------- __inline static float DotProduct(const CVector3D &cVector3D) { return cVector3D.fX * cVector3D.fX + cVector3D.fY * cVector3D.fY + cVector3D.fZ * cVector3D.fZ; } //--------------------------------------------------------------------------------------------- // static float DotProduct(const CVector3D &cVector3D1, const CVector3D &cVector3D2) // // Calculate the dotproduct of the vector with itself //--------------------------------------------------------------------------------------------- __inline static float DotProduct(const CVector3D &cVector3D1, const CVector3D &cVector3D2) { return cVector3D1.fX * cVector3D2.fX + cVector3D1.fY * cVector3D2.fY + cVector3D1.fZ * cVector3D2.fZ; } //--------------------------------------------------------------------------------------------- // static CVector3D CalculateNormal(const CVector3D &v1, const CVector3D &v2, const CVector3D &v3) // // Calculates a normal vector based on 3 vectors //--------------------------------------------------------------------------------------------- __inline static CVector3D CalculateNormal(const CVector3D &v0, const CVector3D &v1, const CVector3D &v2) { CVector3D vNormal; float fNormalLength; vNormal.fX = (v0.fY - v1.fY) * (v0.fZ - v2.fZ) - (v0.fZ - v1.fZ) * (v0.fY - v2.fY); vNormal.fY = (v0.fZ - v1.fZ) * (v0.fX - v2.fX) - (v0.fX - v1.fX) * (v0.fZ - v2.fZ); vNormal.fZ = (v0.fX - v1.fX) * (v0.fY - v2.fY) - (v0.fY - v1.fY) * (v0.fX - v2.fX); fNormalLength = sqrtf(vNormal.fX * vNormal.fX + vNormal.fY * vNormal.fY + vNormal.fZ * vNormal.fZ); vNormal.fX /= fNormalLength; vNormal.fY /= fNormalLength; vNormal.fZ /= fNormalLength; return vNormal; } //--------------------------------------------------------------------------------------------- // float DotProduct() // // Calculate the dot-product of the vector //--------------------------------------------------------------------------------------------- __inline float DotProduct() const { return fX * fX + fY * fY + fZ * fZ; } //--------------------------------------------------------------------------------------------- // float Length() // // Calculates the length of the vector //--------------------------------------------------------------------------------------------- __inline float Length() const { return sqrtf(fX * fX + fY * fY + fZ * fZ); } //--------------------------------------------------------------------------------------------- // void Normalize() // // Normalizes the vector //--------------------------------------------------------------------------------------------- __inline void Normalize() { float fLength; fLength = sqrtf(fX * fX + fY * fY + fZ * fZ); fX /= fLength; fY /= fLength; fZ /= fLength; } //--------------------------------------------------------------------------------------------- // static CVector3D Reflection(const CVector3D& vVector3D, const CVector3D& vNormal) // // Reflects the vector about a normal vector //--------------------------------------------------------------------------------------------- __inline static CVector3D Reflection(const CVector3D& vVector3D, const CVector3D& vNormal) { CVector3D newvector = vVector3D / vVector3D.Length(); return (newvector - vNormal * 2.0f * CVector3D::DotProduct(newvector, vNormal)) * vVector3D.Length(); } //--------------------------------------------------------------------------------------------- // void Reflection(const CVector3D& vNormal) // // Reflects THIS vector about a normal vector //--------------------------------------------------------------------------------------------- __inline void Reflection(const CVector3D& vNormal) { CVector3D newvector = *this / this->Length(); *this = (newvector - vNormal * 2.0f * CVector3D::DotProduct(newvector, vNormal)) * this->Length(); } //--------------------------------------------------------------------------------------------- // void SetVector(const float& fNewX, const float& fNewY, const float& fNewZ) // // Set the data members of the vector //--------------------------------------------------------------------------------------------- __inline void Set(const float &fNewX, const float &fNewY, const float &fNewZ) { fX = fNewX; fY = fNewY; fZ = fNewZ; } void RotateX(const float &fAngle); void RotateY(const float &fAngle); void RotateZ(const float &fAngle); void Scale(const float &fFactor); void Scale(const float &fFactorX, const float &fFactorY, const float &fFactorZ); void TaperX(const float &fRate); void TaperY(const float &fRate); void TaperZ(const float &fRate); void Transform(const float *p_fMatrix); // Has to point to 16 floats void Translate(const float &fTX, const float &fTY, const float &fTZ); // The components are public members for easy access float fX, fY, fZ; // (x, y, z) coordinates for the 3D vector point};#endif

Here is the CPP file

//---------------------------------------------------------------------------------------------// Copyright © 2001 by Nucleus Software, Inc.// All rights reserved.//// $File:: CVector3D.CPP//$Dependencies:: none// $Revision:: 1//$Author:: Ebor Folkertsma// $Date:: 09-24-2001 8:05pm////$Description:: The CVector3D class offers some nice functionality for 3D vectors//---------------------------------------------------------------------------------------------#include "CVector3D.H"#include namespace _CVector3D_{ static CVector3D cVector; // Used for quick transformations static float fCosAngle; static float fSinAngle;}//-------------------------------------------------------------------------------------------------// void RotateX(const float &fAngle)//// This function rotates the vector around the x-axis//// Parameters// fAngle The rotation angle in degrees//-------------------------------------------------------------------------------------------------void CVector3D::RotateX(const float &fAngle){ _CVector3D_::fCosAngle = cosf(fAngle * 0.017453292f); _CVector3D_::fSinAngle = sinf(fAngle * 0.017453292f); _CVector3D_::cVector.fY = fY * _CVector3D_::fCosAngle - fZ * _CVector3D_::fSinAngle; _CVector3D_::cVector.fZ = fY * _CVector3D_::fSinAngle + fZ * _CVector3D_::fCosAngle; fY = _CVector3D_::cVector.fY; fZ = _CVector3D_::cVector.fZ; return;}//-------------------------------------------------------------------------------------------------// void RotateY(const float &fAngle)//// This function rotates the vector around the y-axis//// Parameters// fAngle The rotation angle in degrees//-------------------------------------------------------------------------------------------------void CVector3D::RotateY(const float &fAngle){ _CVector3D_::fCosAngle = cosf(fAngle * 0.017453292f); _CVector3D_::fSinAngle = sinf(fAngle * 0.017453292f); _CVector3D_::cVector.fX = fX * _CVector3D_::fCosAngle + fZ * _CVector3D_::fSinAngle; _CVector3D_::cVector.fZ = fX * -_CVector3D_::fSinAngle + fZ * _CVector3D_::fCosAngle; fX = _CVector3D_::cVector.fX; fZ = _CVector3D_::cVector.fZ; return;}//-------------------------------------------------------------------------------------------------// void RotateZ(const float &fAngle)//// This function rotates the vector around the z-axis//// Parameters// fAngle The rotation angle in degrees//-------------------------------------------------------------------------------------------------void CVector3D::RotateZ(const float &fAngle){ _CVector3D_::fCosAngle = cosf(fAngle * 0.017453292f); _CVector3D_::fSinAngle = sinf(fAngle * 0.017453292f); _CVector3D_::cVector.fX = fX * _CVector3D_::fCosAngle - fY * _CVector3D_::fSinAngle; _CVector3D_::cVector.fY = fX * _CVector3D_::fSinAngle + fY * _CVector3D_::fCosAngle; fX = _CVector3D_::cVector.fX; fY = _CVector3D_::cVector.fY; return;}//-------------------------------------------------------------------------------------------------// void Scale(const float &fFactor)//// This function scales the vector uniform//// Parameters// fFactor The scaling factor//-------------------------------------------------------------------------------------------------void CVector3D::Scale(const float &fFactor){ CVector3D::fX *= fFactor; CVector3D::fY *= fFactor; CVector3D::fZ *= fFactor; return;}//-------------------------------------------------------------------------------------------------// void Scale(const float &fFactorX, const float &fFactorY, const float &fFactorZ)//// This function scales the vector non-uniform//// Parameters//// fFactorX The scale factor for the scaling along the x-axis// fFactorY The scale factor for the scaling along the y-axis// fFactorZ The scale factor for the scaling along the z-axis//-------------------------------------------------------------------------------------------------void CVector3D::Scale(const float &fFactorX, const float &fFactorY, const float &fFactorZ){ CVector3D::fX *= fFactorX; CVector3D::fY *= fFactorY; CVector3D::fZ *= fFactorZ; return;}//------------------------------------------------------------------------------------------------- // void TaperX(const float &fRate)//// This function tapers the vector along the x-axis//// Parameters// fRate The rate of tapering along the x-axis//-------------------------------------------------------------------------------------------------void CVector3D::TaperX(const float &fRate){ CVector3D::fY *= 1.0f + fRate * fX; CVector3D::fZ *= 1.0f + fRate * fX; return;}//------------------------------------------------------------------------------------------------- // void TaperY(const float &fRate)//// This function tapers the vector along the y-axis//// Parameters// fRate The rate of tapering along the y-axis//-------------------------------------------------------------------------------------------------void CVector3D::TaperY(const float &fRate){ CVector3D::fX = 1.0f + fRate * fY; CVector3D::fZ = 1.0f + fRate * fY; return;}//------------------------------------------------------------------------------------------------- // void TaperZ(const float &fRate)//// This function tapers the vector along the z-axis//// Parameters// fRate The rate of tapering along the z-axis//-------------------------------------------------------------------------------------------------void CVector3D::TaperZ(const float &fRate){ CVector3D::fX = 1.0f + fRate * fZ; CVector3D::fY = 1.0f + fRate * fZ; return;}//-------------------------------------------------------------------------------------------------// void Transform(const float *p_fMatrix)//// This function transforms the vector//// Parameters// pMatrix The transformation matrix that is to be applied to the vector (This must be a pointer to a 16 floats array)//-------------------------------------------------------------------------------------------------void CVector3D::Transform(const float *p_fMatrix){ _CVector3D_::cVector.fX = fX * p_fMatrix[0] + fY * p_fMatrix[1] + fZ * p_fMatrix[2] + p_fMatrix[3]; _CVector3D_::cVector.fY = fX * p_fMatrix[4] + fY * p_fMatrix[5] + fZ * p_fMatrix[6] + p_fMatrix[7]; _CVector3D_::cVector.fZ = fX * p_fMatrix[8] + fY * p_fMatrix[9] + fZ * p_fMatrix[10] + p_fMatrix[11]; fX = _CVector3D_::cVector.fX; fY = _CVector3D_::cVector.fY; fZ = _CVector3D_::cVector.fZ; return;}//-------------------------------------------------------------------------------------------------// void Translate(const float &fTX, const float &fTY, const float &fTZ)//// This function translates the vector//// Parameters// fTX The translation along the x-axis// fTY The translation along the y-axis// fTZ The translation along the z-axis//-------------------------------------------------------------------------------------------------void CVector3D::Translate(const float &fTX, const float &fTY, const float &fTZ){ CVector3D::fX += fTX; CVector3D::fY += fTY; CVector3D::fZ += fTZ; return;}`

Please do not mind the bad layouts... it looks decent in my editor!

Hope this was of any help, Dark