Physics and realistic motion in 2 dimensions

[minitech]

I'm making a game where the main character is a white blood cell. Right now I have a circle. 360 points. I want my character to squish against walls, jiggle while moving, etc... but I'm just at a loss as to how to even start doing this. What's the best way to implement that kind of 2-d physics?

[Evil_Giraffe]

Sounds like you want to apply a "damped spring" force between adjacent points. When combined with all your other forces (gravity, collision, etc) it should give you the sort of reaction you're after to the shape of your cell. It won't necessarily cause jiggling while moving, you'd probably have to add in some additional force to set that off.

Once you've got all your forces, it's simply a case of taking the position and velocity of the point, applying the force and working out the position and velocity of the next time slice. You shouldn't have much trouble googling for many resources on that front. The most important piece of advice beyond the mathematics itself is to make sure you divorce "simulation time" from "real world time".

[Milk]

Your learning C right?

Check out the Gish source code.

I believe the blob is defined with 12 points. Each point connects to the opposite point and the 2 adjacent points via virtual springs.

[minitech]

That website is filtered for me because of malicious content, but I'll try looking at it on another computer soon. Thanks.

[minitech]

Okay, I tried making my own spring system based on someone else's advice:

Public Class Particle
        Private _location As PointF
        Private _velocity As PointF
        Private _friction As Single
        Private _frame As RectangleF

        Public Sub New()
            _friction = 0.15!
        End Sub

        Public Property Location() As PointF
            Get
                Return _location
            End Get
            Set(ByVal value As PointF)
                If value.X < _frame.X Then
                    value.X = _frame.X
                ElseIf value.X > _frame.Right Then
                    value.X = _frame.Right
                End If
                If value.Y < _frame.Y Then
                    value.Y = _frame.Y
                ElseIf value.Y > _frame.Bottom Then
                    value.Y = _frame.Bottom
                End If

                _location = value
            End Set
        End Property

        Public Property Velocity() As PointF
            Get
                Return _velocity
            End Get
            Set(ByVal value As PointF)
                _velocity = value
            End Set
        End Property

        Public Property Frame() As RectangleF
            Get
                Return _frame
            End Get
            Set(ByVal value As RectangleF)
                _frame = value
            End Set
        End Property

        Public Sub [Next]()
            _velocity = _velocity.Multiply(1.0! - _friction)
            _location = PointF.Add(_location, New SizeF(_velocity))
        End Sub

        Public Sub MoveTowards(ByVal p As PointF, ByVal from As PointF)
            p = New PointF(p.X - from.X, p.Y - from.Y)
            _velocity = PointF.Add(_velocity.Multiply(0.7!), New SizeF(p.Multiply(0.3!))) '.Limit(5.0!)
        End Sub
    End Class

    Public Class Spring
        Private _defaultDistance As Double
        Private _leniency As Double
        Private _elasticity As Double
        Private _point1, _point2 As Particle

        Public Sub New()
            _leniency = 1.0#
            _elasticity = 0.2#
        End Sub

        Public Property DefaultDistance() As Double
            Get
                Return _defaultDistance
            End Get
            Set(ByVal value As Double)
                _defaultDistance = value
            End Set
        End Property

        Public Property Leniency() As Double
            Get
                Return _leniency
            End Get
            Set(ByVal value As Double)
                _leniency = value
            End Set
        End Property

        Public Property Elasticity() As Double
            Get
                Return _elasticity
            End Get
            Set(ByVal value As Double)
                _elasticity = value
            End Set
        End Property

        Public Property Point1() As Particle
            Get
                Return _point1
            End Get
            Set(ByVal value As Particle)
                _point1 = value
            End Set
        End Property

        Public Property Point2() As Particle
            Get
                Return _point2
            End Get
            Set(ByVal value As Particle)
                _point2 = value
            End Set
        End Property

        Public Sub [Next]()
            Dim distance As Double = Point1.Location.DistanceTo(Point2.Location)
            Dim difference As Double = _defaultDistance - distance
            Dim p1 As New PointF(_point1.Location.X, _point1.Location.Y), _
                p2 As New PointF(_point2.Location.X, _point2.Location.Y)
            Dim dX As Single = (p1.X + p2.X) / 2.0!, _
                dY As Single = (p1.Y + p2.Y) / 2.0!
            p1.X -= dX
            p2.X -= dX
            p1.Y -= dY
            p2.Y -= dY

            If Math.Abs(difference) > _leniency Then
                p1 = p1.Multiply(CSng((1.0# - difference / distance) * _elasticity))
                p2 = p2.Multiply(CSng((1.0# - difference / distance) * _elasticity))
            End If

            _point1.Location = New PointF(p1.X + dX, p1.Y + dY)
            _point2.Location = New PointF(p2.X + dX, p2.Y + dY)
        End Sub
    End Class

However, the cell ends up being squashed instead of being pushed back into a proper circle like it should. The way I set it up is:

Dim f As New RectangleF(-CSng(Game.Width / 2), -CSng(Game.Height / 2), Game.Width, Game.Height)

        For i As Integer = 0 To 359
            Dim x As Single = CSng(Math.Cos(i * Math.PI / 180) * 50), _
                y As Single = CSng(Math.Sin(i * Math.PI / 180) * 50)

            Dim p As New Spring.Particle()
            p.Frame = f
            p.Location = New PointF(x, y)
            particles.Add(p)
        Next

        centerParticle = New Spring.Particle()
        centerParticle.Frame = f

        For i As Integer = 0 To 359
            For j As Integer = i + 1 To 359
                Dim s As New Spring.Spring()
                s.Point1 = particles(i)
                s.Point2 = particles(j)
                s.DefaultDistance = particles(i).Location.DistanceTo(particles(j).Location)
                springs.Add(s)
            Next

            Dim s2 As New Spring.Spring()
            s2.Point1 = particles(i)
            s2.Point2 = centerParticle
            springs.Add(s2)
        Next

Why doesn't it spring properly? How can I make this work?