338.sagews

defaultStartTime  = -1.0
defaultStartForce = 4.0

defaultEndTime    = 2.0
defaultEndForce   = -2.0


def linearForce(time, startTime, startForce, endTime, endForce):
    localTime_a = time - startTime
    localTime_b = time

    if (time < 0):
        return  startForce + (localTime_a * startForce/startTime)
    elif (time == 0):
        return 0
    else:
        return (localTime_b  * endForce/endTime)

def linearForceVelocity(time, startTime, startForce, endTime, endForce):
    #return initialForce*time - (rate/2)*(time ^2)
    #rate = (startForce/startTime)

    localTime_a = time - startTime
    localTime_b = time

    if (time < 0):
        return localTime_a * (startForce + (1/2) * (localTime_a * startForce/startTime))

    elif (time == 0):
        return     1/2 * -startTime * startForce
    else:
        return     1/2 * -startTime * startForce + 1/2 * endForce/endTime * localTime_b^2

def linearForceDisplacement(time, startTime, startForce, endTime, endForce):
    #return (initialForce/2)*(time ^2) - (rate/6)*(time ^3)

    localTime_a = time - startTime
    localTime_b = time

    if (time < 0):

               # localTime_a * (startForce + (1/2) * (localTime_a * startForce/startTime))
               # fx + 1/2 f/t x^2
               # 1/2 fx^2  + 1/6 f/t x^3
               # x^2 (1/2 f + 1/6 f/t x)

        return localTime_a^2 * ((1/2) * startForce + (1/6) * localTime_a * (startForce/startTime))

    elif (time == 0):
        return   (-startTime)^2 * ((1/2) * startForce + (1/6) * -startTime * (startForce/startTime))

    else:
        return   (-startTime)^2 * ((1/2) * startForce + (1/6) * -startTime * (startForce/startTime)) + (localTime_b * 1/2 * -startTime * startForce) + (1/6 * endForce/endTime * localTime_b^3)


def linearForceSingleVariable(n):
    return linearForce(n, defaultStartTime , defaultStartForce ,defaultEndTime, defaultEndForce)
def linearForceVelocitySingleVariable(n):
    return linearForceVelocity(n, defaultStartTime , defaultStartForce ,defaultEndTime, defaultEndForce)
def linearForceDisplacementSingleVariable(n):
    return linearForceDisplacement(n, defaultStartTime , defaultStartForce ,defaultEndTime, defaultEndForce)


linearForcePlot = plot(linearForceSingleVariable, defaultStartTime, defaultEndTime,rgbcolor=hue(0.5))
linearForceVelocityPlot = plot(linearForceVelocitySingleVariable, defaultStartTime, defaultEndTime,rgbcolor=hue(0.1))
linearForceDisplacementPlot = plot(linearForceDisplacementSingleVariable, defaultStartTime, defaultEndTime,rgbcolor=hue(0.3))

show (linearForcePlot + linearForceVelocityPlot + linearForceDisplacementPlot)