vectorfun.style

canvas {
    width = 800
    height = 700
}



const {
    scalar VectorSpaceSize = 350.0
    scalar arrowheadSize = 0.7
    scalar lineThickness = 1.
    scalar arrowThickness = 1.5
    color gray = rgba(0.6, 0.6, 0.6, 1.)
    color lightBlue = rgba(0.2, 0.4, 0.8, 1.0)
    color lightGray = rgba(252, 252, 252, 0.015)
    color green = rgba(0., 0.8, 0., 1.)
    color none = rgba(0., 0., 0., 0.)
    color red = rgba(1,0,0,1)
}

forall VectorSpace U {
    scalar axisSize = const.VectorSpaceSize / 2.0 
    vec2 U.origin = (0.,0.) 
    vec2 o = U.origin 
    U.axisColor = const.gray 

    -- Background
    U.Background = Rectangle {
        center: o
        width: const.VectorSpaceSize
        height: const.VectorSpaceSize
        fillColor: const.lightGray
        strokeColor: const.none
    }

    -- Axis
    U.xaxis = Line {
        start: (o[0]-axisSize, o[1])
        end: (o[0]+axisSize,o[1])
        strokeWidth : const.lineThickness
        style : "solid"
        strokeColor : U.axisColor
        startArrowhead: "straight" -->
        endArrowhead: "straight"
        startArrowheadSize : const.arrowheadSize * 2. 
        endArrowheadSize : const.arrowheadSize * 2.
    }

    -- Y axisx
    U.yaxis = Line {
        start: (o[0], o[1]-axisSize)
        end: (o[0],o[1]+axisSize)
        strokeWidth : const.lineThickness
        style : "solid"
        strokeColor : U.axisColor
        startArrowhead: "straight" -->
        endArrowhead: "straight"
        startArrowheadSize : const.arrowheadSize * 2. 
        endArrowheadSize : const.arrowheadSize * 2.
    }

    U.text = Equation {
        string: U.label 
        center: (o[0] - axisSize, o[1]+axisSize)
        fillColor: U.axisColor
    }
} 
forall Vector u; VectorSpace U 
where In(u,U) {
  /* draw a vector in vector space */
  u.vector = (?,?) 

  u.shape = Line {
    start: U.origin
    end: u.vector
    endArrowhead: "straight"
    strokeColor : const.lightBlue /* or any color you want */
    endArrowheadSize : const.arrowheadSize * 2.
    strokeWidth : 1 -- largeur, bug, strokewidth tied to arrowheadsize
  }

  u.text = Equation {
    string : u.label 
    fillColor : u.shape.strokeColor /* this way it changes accordingly when we change the arrow's color */
    }

    -- constraints : given enough constraints, impossible to use ? for the scalar value
    ensure contains(U.Background,u.shape)
    ensure contains(U.Background,u.text) 
    ensure disjoint(u.shape,u.text)
    ensure vdist(u.shape.end, u.text.center) < 20
    ensure disjoint(u.shape,u.text, 10.0)
    
    layer u.text above U.xaxis
    layer u.text above U.yaxis
}


-- definition des scalaires
forall Scalar a {
    a.scalar = ?
    --a.scalar = 5 -- if the scalar value is not set to a random one but fixed, can get the compiler to run 
    ensure inRange(a.scalar,2.,5.)
}

-- definition de la multiplication
forall Vector u; Scalar a; Vector v; VectorSpace U
where u := multiply(a,v); In(u,U); In(v,U) {
    override u.vector = (a.scalar * v.vector[0], a.scalar * v.vector[1])
---    override u.vector = (a.scalar * v.vector)
---    override u.shape.end = a.scalar * (v.shape.end - U.origin) + U.origin
---    override u.shape.end = (a.scalar * (v.shape.end[0]- U.origin[0]) + U.origin[0],a.scalar * (v.shape.end[1]- U.origin[1]) + U.origin[1])

    override u.shape.strokeColor = const.red
}