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Posted 4 Oct 2009

A New Perspective on Viewing

, 6 Oct 2009 CPOL
Simple yet comprehensive viewing code for OpenGL and Direct3D.
// Interact.cpp
// Simple 3D interaction
// Copyright (C) 2009 John Hilton
// Considerable use of the SpatialMath types and operators is used to greatly
// simplify the code. An understanding of SpatialMath's operators is needed to
// read the code.

#include <stdafx.h>
#include "gfx.h"
#include "interact.h"
#include "spatialmath.h"

template< typename T > union AVec2 { T v2[2]; T x, y; };
typedef AVec2<float> AVec2f;

class CInteractImpl
    POINTS          m_LastMouse;
    AVec3f          m_MovedFrom;    // view space point
    AVec3f          m_MovedTo;      // view space point
    TViewVolumef   *m_pViewVolume;
    AMat4x3f       *m_pViewToWorld;
    float           m_PixelToViewRectFactor;
    static const float m_kVerySmall;

    void OnLmbDown( POINTS& MousePos )
        // Update m_LastMouse
        m_LastMouse = MousePos;
    BOOL OnMouseMove( HWND hWnd, UINT nFlags, POINTS& MousePos, float ViewVolume[7], float ViewToWorld[4][3] )
        // Ignore the mouse move unless the left mouse button is down
        if (~nFlags & MK_LBUTTON)
            return FALSE;

        // Save the parameters
        m_pViewVolume    = (TViewVolumef *) ViewVolume;
        m_pViewToWorld   = (AMat4x3f*) ViewToWorld;

        // Calculate the pixel-to-view-rectangle scale factor
        RECT rect;
        GetClientRect( hWnd, &rect );
        m_PixelToViewRectFactor = m_pViewVolume->hw * 2.0f / rect.right;

        // Transform the mouse move from the physical pixel space with the
        // origin at the top left to the virtual view space on the z=0 plane.
        m_MovedTo.x   =   MousePos.x * m_PixelToViewRectFactor - m_pViewVolume->hw;
        m_MovedTo.y   = -(MousePos.y * m_PixelToViewRectFactor - m_pViewVolume->hh);
        m_MovedTo.z   = 0;
        m_MovedFrom.x =   m_LastMouse.x * m_PixelToViewRectFactor - m_pViewVolume->hw;
        m_MovedFrom.y = -(m_LastMouse.y * m_PixelToViewRectFactor - m_pViewVolume->hh);
        m_MovedFrom.z = 0;

        // Update m_LastMouse
        m_LastMouse = MousePos;

        // Select either Pan, ZoomSpinZ or Spin
        BOOL Redraw;
        if (nFlags & MK_CONTROL)        Redraw = SpinXY();
        else if (nFlags & MK_SHIFT)     Redraw = ZoomSpinZ();
        else                            Redraw = Pan();

        // forget the parameters
        m_pViewVolume = NULL;
        m_pViewToWorld = NULL;

        return Redraw;

    BOOL Pan()
        // Calculate the view space pan vector, transform it to world space
        // and subtract it from the ViewToWorld.trn
        m_pViewToWorld->trn -= (m_MovedTo - m_MovedFrom) * m_pViewToWorld->rot;
        return TRUE;

    BOOL ZoomSpinZ()
        // This is similar interaction to the modern multitouch screen interaction
        // of 2D images with one finger at the center of the screen. Casual User's
        // prefer zoom as an independent interaction.

        float MovedFromLength = LENGTH m_MovedFrom;
        float MovedToLength   = LENGTH m_MovedTo;
        if (abs(MovedFromLength) < m_kVerySmall || abs(MovedToLength) < m_kVerySmall)
            return FALSE;

        // Calculate the spin angle
        float SpinAngle = atan2( m_MovedTo.y  , m_MovedTo.x )
                        - atan2( m_MovedFrom.y, m_MovedFrom.x );

        // Calculate the view space z-axis rotation matrix
        float cs = cos(SpinAngle);
        float sn = sin(SpinAngle);
        AMat3x3f Spin = CMat3x3f( cs, -sn, 0,
                                  sn,  cs, 0,
                                   0,  0, 1 );

        // Rotate about the view space origin (world space m_pViewToWorld.trn stays put)
        m_pViewToWorld->rot = Spin * m_pViewToWorld->rot;

        // Calculate the inverse zoom factor
        float InverseZoomFactor = MovedFromLength / MovedToLength;

        // Zoom about the view space origin
        m_pViewVolume->hw *= InverseZoomFactor;
        m_pViewVolume->hh *= InverseZoomFactor;

        return TRUE;
    BOOL SpinXY()
        // Provide rotation so horizontal movement corresponds to a
        // vertical spin and vertical movement corresponds to a horizontal
        // spin.

        AVec3f Delta = m_MovedTo - m_MovedFrom;
        float LengthDelta = LENGTH Delta;
        if (LengthDelta < m_kVerySmall)
            return FALSE;
        Delta /= LengthDelta;   // make a unit vector

        // Say that moving 1/4 of the longest of the Window's width or height
        // equals one rotation.
        float HalfRotationDistance = max( m_pViewVolume->hw, m_pViewVolume->hh );
        float SpinAngle = LengthDelta * (float) M_PI / HalfRotationDistance;

        // Calculate the view space spin axis
        AVec3f SpinAxis = CVec3f(0,0,1) CROSS Delta;

        // Rotate about the view space origin (world space m_pViewToWorld.trn stays put)
        m_pViewToWorld->rot = CMat3x3f( SpinAngle, SpinAxis ) * m_pViewToWorld->rot;

        return TRUE;
const float CInteractImpl::m_kVerySmall = 1e-6f;

#pragma region CInteract

    m_pImpl = new CInteractImpl;
    ASSERT( m_pImpl );

    if (m_pImpl) delete m_pImpl;

void CInteract::OnLbuttonDown( POINTS& MousePos )
    m_pImpl->OnLmbDown( MousePos );

BOOL CInteract::OnMouseMove( HWND hWnd, UINT nFlags, POINTS& MousePos,
                             float ViewVolume[7], float ViewToWorld[4][3] )
    return m_pImpl->OnMouseMove( hWnd, nFlags, MousePos, ViewVolume, ViewToWorld );

#pragma endregion

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About the Author

John Hilton
Founder Spatial Freedom
Australia Australia
Software engineer, mechanical engineer, electronics engineer, inventor, manager, entrepreneur, husband, father, friend.
B.Sc. B.E.(Hons) M.Eng.Sc.
Some things I've done
- Invented the Spaceball(R)/1983 and Astroid(R)/2002 3D mice
- Patents: 3D mouse, data compression, acoustic transducer
- Wrote animation software in mid 1980s for TV commercials
- Wrote a basic CAD drawing program in 1980s
- Lived in Boston, Massachusetts for 11 years
- Architected and managed full custom ASIC chip
- Reviewed bionic eye technology for investment purposes
- Product development on CPR aid for heart attacks
- Developed an electronic sports whistle
- Was actually stranded on a deserted Pacific island
- Software: lots - embedded, device driver, applications
Some things I want to do
- Develop more cool hardware/software products
- Solve the 3D mouse software barrier to proliferate 3D mice
- Help bring 3D to the masses
- Help others

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