• Create Account

### #Actualslicer4ever

Posted 10 February 2013 - 12:44 PM

if you have a normalized direction vector.

and a point, let's say:

Dir Vector = (1.0, 0.0, 0.0)

Point = (20.0, 10.0, 0.0)

the closest point on the line would be: (Dir.x*Point.x, Dir.y*Point.y, Dir.z*Point.z) (20.0, 0.0, 0.0)

let's say he have an arbitrary direction:

Dir Vector = (0.707, 0.707, 0.0)

Point = (20.0, 10.0, 0.0)

Line Point = (14.14, 7.07, 0.0)

now then, to figure out if the point is on the line, or outside the line:

let's say we have a line start point at: (5.0, 0.0, 0.0), and end point: (10.0, 0.0, 0.0)

this means we have a normalized direction of: (1.0, 0.0, 0.0).

we
also need to take the dot product of the direction vector and the
start/end points to check that the tested vertex is on the line(this
essentially becomes a plane equation):

(5.0*1.0 + 0.0*0.0 + 0.0*0.0) =   5

(10.0f*1.0 + 0.0*0.0 + 0.0*0.0) = 10

so, let's try 2 points: (20.0, 30.0, 0.0), and (0.0f, 30.0, 0.0).

These get plotted on the line to be: (20.0, 0.0, 0.0), and (0.0, 0.0, 0.0)

so, now we get the resulting point's dot product with the direction vector: (20*1 + 0*0 + 0*0)
= 20.  we check that this value is inside the start/end point's dot
products, if it's > or < than one or the other, it means it's past
that point.  as such the closest point to that line is at the end
point, and so, we return (10.0, 0.0, 0.0) as the closest point on the
line to the vertex.

(0.0, 0.0, 0.0) is 0 when you
take the dot product of the directional line, it is < 5, so that
means we take the start point as the closest point on a line to the vertex.

so the code would like:

struct Vector3{
float x,y,z;

float Dot(Vector3 &O){
return x*O.x+y*O.y+z*O.z;
}

Vector3 Normalize(void){
float d = sqrtf(x*x+y*y+z*z);
if(d<=0.00001f) return Vector3(x,y,z);
d = 1.0f/d;
return Vector3(x*d, y*d, z*d);
}
//assume operator overloads for +, -, *, and constructor'sthat take's 3 floats.
};

Vector3 ClosestPoint(Vector3 &LineStart, Vector3 &LineEnd, Vector3 &Point){
Vector3 Direction = (LineEnd-LineStart).Normalize();
float LineBDot = Direction.Dot(LineEnd);
Vector3 LinePoint = Point*Direction;
float LinePointDot = Direction.Dot(LinePoint);
//check which way we need to compare LinePointDot with B and A dot products:
if(LinePointDot>LineBDot) return LineEnd;
}else{
if(LinePointDot<LineBDot) return LineEnd;
}
return LinePoint;
}



^^untested^^

that *should* work, but someone correct me if i just went on a completely lunatic babble that makes absolutely no sense.

edit: i should have checked out what JTippetts linked to first.

### #1slicer4ever

Posted 10 February 2013 - 12:43 PM

if you have a normalized direction vector.

and a point, let's say:

Dir Vector = (1.0, 0.0, 0.0)

Point = (20.0, 10.0, 0.0)

the closest point on the line would be: (Dir.x*Point.x, Dir.y*Point.y, Dir.z*Point.z) (20.0, 0.0, 0.0)

let's say he have an arbitrary direction:

Dir Vector = (0.707, 0.707, 0.0)

Point = (20.0, 10.0, 0.0)

Line Point = (14.14, 7.07, 0.0)

now then, to figure out if the point is on the line, or outside the line:

let's say we have a line start point at: (5.0, 0.0, 0.0), and end point: (10.0, 0.0, 0.0)

this means we have a normalized direction of: (1.0, 0.0, 0.0).

we
also need to take the dot product of the direction vector and the
start/end points to check that the tested vertex is on the line(this
essentially becomes a plane equation):

(5.0*1.0 + 0.0*0.0 + 0.0*0.0) =   5

(10.0f*1.0 + 0.0*0.0 + 0.0*0.0) = 10

so, let's try 2 points: (20.0, 30.0, 0.0), and (0.0f, 30.0, 0.0).

These get plotted on the line to be: (20.0, 0.0, 0.0), and (0.0, 0.0, 0.0)

so, now we get the resulting point's dot product with the direction vector: (20*1 + 0*0 + 0*0)
= 20.  we check that this value is inside the start/end point's dot
products, if it's > or < than one or the other, it means it's past
that point.  as such the closest point to that line is at the end
point, and so, we return (10.0, 0.0, 0.0) as the closest point on the
line to the vertex.

(0.0, 0.0, 0.0) is 0 when you
take the dot product of the directional line, it is < 5, so that
means we take the start point as the closest point on a line to the vertex.

so the code would like:

struct Vector3{
float x,y,z;

float Dot(Vector3 &O){
return x*O.x+y*O.y+z*O.z;
}

Vector3 Normalize(void){
float d = sqrtf(x*x+y*y+z*z);
if(d<=0.00001f) return Vector3(x,y,z);
d = 1.0f/d;
return Vector3(x*d, y*d, z*d);
}
//assume operator overloads for +, -, *, and constructor'sthat take's 3 floats.
};

Vector3 ClosestPoint(Vector3 &LineStart, Vector3 &LineEnd, Vector3 &Point){
Vector3 Direction = (LineEnd-LineStart).Normalize();
float LineBDot = Direction.Dot(LineEnd);
Vector3 LinePoint = Point*Direction;
float LinePointDot = Direction.Dot(LinePoint);
//check which way we need to compare LinePointDot with B and A dot products:
if(LinePointDot>LineBDot) return LineEnd;
}else{
if(LinePointDot<LineBDot) return LineEnd;
}
return LinePoint;
}



^^untested^^

that *should* work, but someone correct me if i just went on a completely lunatic babble that makes absolutely no sense.

PARTNERS