CODEWITHSUNDEEP
javaopengl
Tschallacka
Tschallacka

Reputation: 28742

Extrapolate a line beyond two known points

I really suck at math. No, better explanation: I don't know how to interpret mathematical notation. My brain just cant interpret it. That's why I come to the programming community for help "translating" math into a language I do understand.

I have two sets of coordinates in 3d space representing the line of sight.

Vector1(eyes) x=10 y=10 z=4
Vector2(lookingat) x=10 y=8 z=4.785

How do I calculate a point with these double values beyond the looking at value? for example, what lies 2 points beyond the line we are looking it? what location in space would that be?

In short:

How do I extrapolate a given point beyond the line made up by two vectors with given double value along the line.

a known
 \
  \
   \
    b known
     ?    
      ?     + 3
       ?
        c what is this value...

Edit

With the help of the answer of @Thrustmaster I came up with this wonderfull solution. Thanks a lot :D

private Vec3 calculateLine(Vec3 x1, Vec3 x2, double distance) {
    double length = Math.sqrt(multiply(x2.xCoord - x1.xCoord) + multiply((x2.yCoord - x1.yCoord)) + multiply((x2.zCoord - x1.zCoord)));
    double unitSlopeX = (x2.xCoord-x1.xCoord) / length;
    double unitSlopeY = (x2.yCoord-x1.yCoord) / length;
    double unitSlopeZ = (x2.zCoord-x1.zCoord) / length;
    double x = x1.xCoord + unitSlopeX * distance;
    double y = x1.yCoord + unitSlopeY * distance;
    double z = x1.zCoord + unitSlopeZ * distance;
    return Vec3.createVectorHelper(x, y, x);
}
private double multiply(double one) {
    return one * one;
}

Upvotes: 1

Views: 2283

Answers (1)

UltraInstinct
UltraInstinct

Reputation: 44454

You need to start looking to basic 3D coordinate geometry.

In 3D, the equation can be written as:

x = x1 + unitSlopeX * distance
y = y1 + unitSlopeY * distance
z = z1 + unitSlopeZ * distance

.. where (x1,y1,z1) can be any point on the line; in this case (10,10,4).

Next set of unknowns is all 3 unitSlopes. To calculate it, simply subtract the two points (this will ive you a vector), and divide by the length of the vector.

length = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
unitSlopeX = (x2-x1) / length
unitSlopeY = (y2-y1) / length
unitSlopeZ = (z2-z1) / length

Now, to finally, get your third coordinate, simply plug in distance (any value) into the three equations at the beginning of this post.

In vector notation:

V = V1 + t * (V2 - V1) / | V2 - V1 |

.. where t is any real number.

Upvotes: 7

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