Projecting vectors

[EthernautParticipant]

How do I take a Vec3 coordinate and “project” it onto the 2D camera plane?

I’m trying to draw HUD elements on top of a 3D scene that stay locked to their 3D counterparts. Going through the modules I see that the camera has a Matrix and I can multiply the point by that, but I don’t know how to proceed from there and get the actual projected point as Vec2.

Thanks!

[Mark SiblyKeymaster]

Dividing a 3d point by it’s ‘z’ component will give you a 2d point at z=1.

[EthernautParticipant]

Ok, almost working…

The line translates across the screen as the camera rotates, but at a different rate. I imagine this is because I’m using the camera’s Matrix but not the ProjectionMatrix, so the FOV is ignored. But a ProjectionMatrix is Mat4, and I don’t see any method there that could help me in this case. Or is there?

Monkey

#Import "<mojo3d>" Using std.. Using mojo.. Using mojo3d.. Function Main() New AppInstance New TestWindow App.Run() End Class TestWindow Extends Window Field refBall:Model Field camera:Camera Field light:Light Method New() Super.New( "Test", 1280, 720, WindowFlags.Resizable ) ClearColor = Color.Black Layout = "fill" refBall = Model.CreateSphere( 1, 30,30, New PbrMaterial( Color.Orange, 0, 0.5 ) ) camera = New Camera camera.Move( 0, 2, -5 ) camera.Near = 0.1 camera.Far = 10.0 camera.PointAt( New Vec3f ) light = New Light light.Rotation = New Vec3f( 30, 60, 0 ) End Method OnRender( canvas:Canvas ) Override App.RequestRender() If Keyboard.KeyDown( Key.Right ) camera.Ry -= 1.0 Else If Keyboard.KeyDown( Key.Left ) camera.Ry += 1.0 End If Keyboard.KeyDown( Key.Up ) camera.Rx -= 1.0 Else If Keyboard.KeyDown( Key.Down ) camera.Rx += 1.0 End Scene.GetCurrent().Render( canvas, camera ) Draw3DLine( canvas, camera, Width, Height, New Vec3f(0,-1,0), New Vec3f(0,1,0) ) End Function Draw3DLine( canvas:Canvas, camera:Camera, width:Float, height:Float, v0:Vec3f, v1:Vec3f ) Local c0 := ( -camera.Matrix*v0 ) Local c1 := ( -camera.Matrix*v1 ) Local offsetX := width/2.0 Local offsetY := height/2.0 Local s0 := New Vec2f( ((c0.x/c0.z)*width)+offsetX, ((c0.y/-c0.z)*height)+offsetY ) Local s1 := New Vec2f( ((c1.x/c1.z)*width)+offsetX, ((c1.y/-c1.z)*height)+offsetY ) canvas.DrawLine( s0, s1 ) End End

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#Import "<mojo3d>"   Using std.. Using mojo.. Using mojo3d..   Function Main() New AppInstance New TestWindow App.Run() End     Class TestWindow Extends Window Field refBall:Model Field camera:Camera Field light:Light Method New() Super.New( "Test", 1280, 720, WindowFlags.Resizable ) ClearColor = Color.Black Layout = "fill" refBall = Model.CreateSphere( 1, 30,30, New PbrMaterial( Color.Orange, 0, 0.5 ) )   camera = New Camera camera.Move( 0, 2, -5 ) camera.Near = 0.1 camera.Far = 10.0 camera.PointAt( New Vec3f ) light = New Light light.Rotation = New Vec3f( 30, 60, 0 ) End Method OnRender( canvas:Canvas ) Override App.RequestRender() If Keyboard.KeyDown( Key.Right ) camera.Ry -= 1.0 Else If Keyboard.KeyDown( Key.Left ) camera.Ry += 1.0 End If Keyboard.KeyDown( Key.Up ) camera.Rx -= 1.0 Else If Keyboard.KeyDown( Key.Down ) camera.Rx += 1.0 End Scene.GetCurrent().Render( canvas, camera ) Draw3DLine( canvas, camera, Width, Height, New Vec3f(0,-1,0), New Vec3f(0,1,0) ) End Function Draw3DLine( canvas:Canvas, camera:Camera, width:Float, height:Float, v0:Vec3f, v1:Vec3f ) Local c0 := ( -camera.Matrix*v0 ) Local c1 := ( -camera.Matrix*v1 ) Local offsetX := width/2.0 Local offsetY := height/2.0 Local s0 := New Vec2f( ((c0.x/c0.z)*width)+offsetX, ((c0.y/-c0.z)*height)+offsetY ) Local s1 := New Vec2f( ((c1.x/c1.z)*width)+offsetX, ((c1.y/-c1.z)*height)+offsetY ) canvas.DrawLine( s0, s1 ) End End

[Mark SiblyKeymaster]

Ok, I think these camera methods are basically what you’re after? Adding to repos soon…

Monkey

#rem monkeydoc Converts a point from world coordinates to viewport coordinates. #end Method ProjectToViewport:Vec2f( worldVertex:Vec3f ) Local clip_coords:=ProjectionMatrix * InverseMatrix * New Vec4f( worldVertex,1.0 ) Local ndc_coords:=clip_coords.XY/clip_coords.w Local vp_coords:=Cast<Vec2f>( Viewport.Size ) * (ndc_coords * 0.5 + 0.5) Return vp_coords End #rem monkeydoc Converts a point from viewport coordinates to world coordinates. #end Method UnprojectFromViewport:Vec3f( viewportCoords:Vec2f ) Local vp_coords:=viewportCoords / Cast<Vec2f>( Viewport.Size ) * 2.0 - 1.0 Local clip_coords:=New Mat4f( Matrix ) * -ProjectionMatrix * New Vec4f( vp_coords,-1.0,1.0 ) Local world_coords:=clip_coords.XYZ/clip_coords.w Return world_coords End

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#rem monkeydoc Converts a point from world coordinates to viewport coordinates. #end Method ProjectToViewport:Vec2f( worldVertex:Vec3f )   Local clip_coords:=ProjectionMatrix * InverseMatrix * New Vec4f( worldVertex,1.0 ) Local ndc_coords:=clip_coords.XY/clip_coords.w Local vp_coords:=Cast<Vec2f>( Viewport.Size ) * (ndc_coords * 0.5 + 0.5) Return vp_coords End #rem monkeydoc Converts a point from viewport coordinates to world coordinates. #end Method UnprojectFromViewport:Vec3f( viewportCoords:Vec2f ) Local vp_coords:=viewportCoords / Cast<Vec2f>( Viewport.Size ) * 2.0 - 1.0 Local clip_coords:=New Mat4f( Matrix ) * -ProjectionMatrix * New Vec4f( vp_coords,-1.0,1.0 ) Local world_coords:=clip_coords.XYZ/clip_coords.w Return world_coords End

You can added these as extensoin methods if you want, or butcher them for your own evil purposes.

[nerobotParticipant]

Is there a plan to add switcher for camera orthographic / perspective mode?

[EthernautParticipant]

Sweet! Thanks!

Is there a plan to add switcher for camera orthographic / perspective mode?

That would be great. I tried doing it by butchering the existing classes and failed miserably!

Here’s the working version of the 3D lines example, if anyone is interested…

Monkey

#Import "<mojo3d>" Using std.. Using mojo.. Using mojo3d.. Function Main() New AppInstance New TestWindow App.Run() End Class TestWindow Extends Window Field refBall:Model Field camera:Camera Field light:Light Method New() Super.New( "Test", 1280, 720, WindowFlags.Resizable ) ClearColor = Color.Black Layout = "fill" refBall = Model.CreateSphere( 1, 30,30, New PbrMaterial( Color.Orange, 0, 0.5 ) ) camera = New Camera camera.Move( 0, 0, -5 ) camera.Near = 0.1 camera.Far = 10.0 camera.FOV = 60 camera.PointAt( New Vec3f ) light = New Light light.Rotation = New Vec3f( 30, 60, 0 ) End Method OnRender( canvas:Canvas ) Override App.RequestRender() If Keyboard.KeyDown( Key.Right ) camera.Ry -= 1.0 Else If Keyboard.KeyDown( Key.Left ) camera.Ry += 1.0 End If Keyboard.KeyDown( Key.Up ) camera.Rx -= 1.0 Else If Keyboard.KeyDown( Key.Down ) camera.Rx += 1.0 End Scene.GetCurrent().Render( canvas, camera ) canvas.DrawText( "Use cursor keys to rotate camera", 10, 10 ) Draw3DLine( canvas, camera, New Vec3f(-1,-1,0), New Vec3f(1,-1,0) ) Draw3DLine( canvas, camera, New Vec3f(1,-1,0), New Vec3f(1,1,0) ) Draw3DLine( canvas, camera, New Vec3f(1,1,0), New Vec3f(-1,1,0) ) Draw3DLine( canvas, camera, New Vec3f(-1,1,0), New Vec3f(-1,-1,0) ) End Method Draw3DLine( canvas:Canvas, camera:Camera, v0:Vec3f, v1:Vec3f ) Local s0 := camera.ProjectToView( v0 ) Local s1 := camera.ProjectToView( v1 ) canvas.DrawLine( s0.X, -s0.Y+Height, s1.X, -s1.Y+Height ) End End Class Camera Extension Method ProjectToView:Vec2f( worldVertex:Vec3f ) Local clip_coords:=ProjectionMatrix * InverseMatrix * New Vec4f( worldVertex,1.0 ) Local ndc_coords:=clip_coords.XY/clip_coords.w Local vp_coords:=Cast<Vec2f>( Viewport.Size ) * (ndc_coords * 0.5 + 0.5) Return vp_coords End End

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#Import "<mojo3d>"   Using std.. Using mojo.. Using mojo3d..   Function Main() New AppInstance New TestWindow App.Run() End     Class TestWindow Extends Window Field refBall:Model Field camera:Camera Field light:Light Method New() Super.New( "Test", 1280, 720, WindowFlags.Resizable ) ClearColor = Color.Black Layout = "fill" refBall = Model.CreateSphere( 1, 30,30, New PbrMaterial( Color.Orange, 0, 0.5 ) )   camera = New Camera camera.Move( 0, 0, -5 ) camera.Near = 0.1 camera.Far = 10.0 camera.FOV = 60 camera.PointAt( New Vec3f ) light = New Light light.Rotation = New Vec3f( 30, 60, 0 ) End Method OnRender( canvas:Canvas ) Override App.RequestRender() If Keyboard.KeyDown( Key.Right ) camera.Ry -= 1.0 Else If Keyboard.KeyDown( Key.Left ) camera.Ry += 1.0 End If Keyboard.KeyDown( Key.Up ) camera.Rx -= 1.0 Else If Keyboard.KeyDown( Key.Down ) camera.Rx += 1.0 End   Scene.GetCurrent().Render( canvas, camera ) canvas.DrawText( "Use cursor keys to rotate camera", 10, 10 ) Draw3DLine( canvas, camera, New Vec3f(-1,-1,0), New Vec3f(1,-1,0) ) Draw3DLine( canvas, camera, New Vec3f(1,-1,0), New Vec3f(1,1,0) ) Draw3DLine( canvas, camera, New Vec3f(1,1,0), New Vec3f(-1,1,0) ) Draw3DLine( canvas, camera, New Vec3f(-1,1,0), New Vec3f(-1,-1,0) ) End Method Draw3DLine( canvas:Canvas, camera:Camera, v0:Vec3f, v1:Vec3f ) Local s0 := camera.ProjectToView( v0 ) Local s1 := camera.ProjectToView( v1 ) canvas.DrawLine( s0.X, -s0.Y+Height, s1.X, -s1.Y+Height ) End End   Class Camera Extension Method ProjectToView:Vec2f( worldVertex:Vec3f ) Local clip_coords:=ProjectionMatrix * InverseMatrix * New Vec4f( worldVertex,1.0 ) Local ndc_coords:=clip_coords.XY/clip_coords.w Local vp_coords:=Cast<Vec2f>( Viewport.Size ) * (ndc_coords * 0.5 + 0.5) Return vp_coords End End

[Mark SiblyKeymaster]

Yes, camera’ll eventually support orthographic, and hopefully stero one day!

This is the nice thing about the 4×4 projection matrix – it supports both perspective and orthographic projections so the project/unproject code wont have to change.

[Author]

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