ofVec2f
ofVec2f is a class for storing a two dimensional vector.
Moving through space requires knowledge of where things are and where they are going. Vector Maths is the class of mathematics that gives us control over these things in space, allowing for elegant and intuitive descriptions of complex structures and movement. Vectors are at the heart of animations, particle systems, and 2D and 3D graphics.
Vectors in mathematics in general are entities with magnitude (also called length) and direction. A vector whose magnitude is 1 (ie a vector that is normalized) is called a unit vector. Unit vectors are very handy for storing directions as they can be easily scaled up (or down) to represent motion in a particular direction with a particular length.
You will also see the term vector used to describe an array of objects in C++ (such as text strings). Don't let this confuse you, they are quite different: one of them is a mathematical term for a fixed-length list of numbers that you can do mathematical operations on, the other is a C++-specific term that means 'dynamically sizeable array'.
ofVec2f has two member variables, x and y, which allow to conveniently store 2D properties of an object such as its position, velocity, or acceleration.
ofVec2f v1; // v1.x is 0, v1.y is 0
v1.set( 10, 50 ); // now v1.x is 10, v1.y is 50
Using ofVec2f greatly simplifies arithmetic operations in two dimensions. For example if you have two vectors v1 and v2, both of which represent a 2D change in position, you can find the total change of position of both of them just by doing an addition v1 + v2:
ofVec2f v1(5, 2); // v1 represents walking 5 steps forward then 2 steps sideways
ofVec2f v2;
v2.set(1, 1); // v2 represents walking 1 step forward then 1 step sideways
// what happens if you do v1 followed by v2? just add v1 and v2 together:
ofVec2f result = v1 + v2; // result is 6 steps forward then 3 steps sideways
You can scale an ofVec2f by multiplying it with a float:
ofVec2f v1(5, 2); // walk 5 steps forward and 2 steps right
// what happens if we do v1 three times?
ofVec2f result = v1 * 3; // result is 15 steps forward and 6 steps right
This also works for subtraction and division.
As you can see this really makes dealing with vectors as easy as dealing with single floats or ints, and can reduce the number of lines of code you have to write by half, at the same time making your code much easier to read and understand!
align(...)
bool ofVec2f::align(const ofVec2f &vec, float tolerance=0.0001)
Returns true if both vectors are aligned (pointing in the same direction). tolerance is an angle tolerance/threshold (specified in degrees) for deciding if the vectors are sufficiently aligned.
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(4, 2);
// v1.align(v2) returns true
alignRad(...)
bool ofVec2f::alignRad(const ofVec2f &vec, float tolerance=0.0001)
Just like align but the angle tolerance is specified in radians rather than degrees.
angle(...)
float ofVec2f::angle(const ofVec2f &vec)
Calculate and return the angle in degrees between this vector and vec.
ofVec2f v1(1,0);
ofVec2f v2(0,1);
float angle = v1.angle(v2); // angle is 90
angleRad(...)
float ofVec2f::angleRad(const ofVec2f &vec)
Calculate and return the angle in radians between this vector and vec.
ofVec2f v1(1,0);
ofVec2f v2(0,1);
float angle = v1.angleRad(v2); // angle is HALF_PI
average(...)
ofVec2f ofVec2f::average(const ofVec2f *points, int num)
Sets this vector to be the average (centre of gravity or centroid) of a given array of ofVec2fs. points is the array of ofVec2fs and num specifies the number of ofVec2fs in the array.
int numPoints = 10;
ofVec2f points[numPoints];
for ( int i=0; i<numPoints; i++ ) {
points[i].set( ofRandom(0,100), ofRandom(0,100) );
}
ofVec2f centroid;
centroid.average( points, numPoints );
// centroid now is the centre of gravity/average of all the random points
distance(...)
float ofVec2f::distance(const ofVec2f &pnt)
Treats both this vector and pnt as points in 2D space, and calculates and returns the distance between them.
ofVec2f p1( 3, 4 );
ofVec2f p2( 6, 8 );
float distance = p1.distance( p2 ); // distance is 5
distance involves a square root calculation, which is one of the slowest things you can do in programming. If you don't need an exact number but rather just a rough idea of distance (for example when finding the shortest distance of a bunch of points to a reference point, where it doesn't matter exactly what the distances are, you just want the shortest), you can use squareDistance instead.
dot(...)
float ofVec2f::dot(const ofVec2f &vec)
Calculate and return the dot product of this vector with vec.
Dot product (less commonly known as Euclidean inner product) expresses the angular relationship between two vectors. In other words it is a measure of how parallel two vectors are. If they are completely perpendicular the dot product is 0; if they are completely parallel their dot product is either 1 if they are pointing in the same direction, or -1 if they are pointing in opposite directions.
Image courtesy of Wikipedia
ofvec2f a1(1, 0);
ofVec2f b1(0, 1); // 90 degree angle to a1
dot = a1.dot(b1); // dot is 0, ie cos(90)
ofVec2f a2(1, 0);
ofVec2f b2(1, 1); // 45 degree angle to a2
b2.normalize(); // vectors should to be unit vectors (normalized)
float dot = a2.dot(b2); // dot is 0.707, ie cos(45)
ofVec2f a3(1, 0);
ofVec2f b3(-1, 0); // 180 degree angle to a3
dot = a3.dot(b3); // dot is -1, ie cos(180)
getInterpolated(...)
ofVec2f ofVec2f::getInterpolated(const ofVec2f &pnt, float p)
Perform a linear interpolation of this vector's position towards pnt and return the interpolated position without altering the original vector. p controls the amount to move towards pnt. p is normally between 0 and 1 and where 0 means stay the original position and 1 means move all the way to pnt, but you can also have p greater than 1 overshoot pnt, or less than 0 to move backwards away from pnt.
ofVec2f v1( 0, 5 );
ofVec2f v2( 10, 10 );
ofVec3f v3 = v1.getInterpolated( p2, 0.5 ); // v3 is (5, 7.5)
ofVec3f v4 = v1.getInterpolated( p2, 0.8 ); // v4 is (8, 9)
getLimited(...)
ofVec2f ofVec2f::getLimited(float max)
Return a copy of this vector with its length (magnitude) restricted to a maximum of max units by scaling down if necessary.
ofVec2f v1(5, 1); // length is about 5.1
ofVec2f v2(2, 1); // length is about 2.2
ofVec2f v1Limited = v1.getLimited(3);
// v1Limited is (2.9417, 0.58835) which has length of 3 in the same direction as v1
ofVec2f v2Limited = v2.getLimited(3);
// v2Limited is (2, 1) (same as v2)
getMiddle(...)
ofVec2f ofVec2f::getMiddle(const ofVec2f &pnt)
Calculate and return the midpoint between this vector and pnt.
ofVec2f v1(5, 0);
ofVec2f v2(10, 10);
ofVec3f mid = v1.getMiddle(v2); // mid gets (7.5, 5)
getNormalized()
ofVec2f ofVec2f::getNormalized()
Return a normalized copy of this vector.
Normalization means to scale the vector so that its length (magnitude) is exactly 1, at which stage all that is left is the direction. A normalized vector is usually called a unit vector, and can be used to represent a pure direction (heading).
ofVec2f v1(5, 0);
ofVec2f v1Normalized = v1.getNormalized(); // (1, 0)
ofVec2f v2(5, 5);
ofVec2f v2Normalized = v2.getNormalized(); // (√2, √2)
getPerpendicular()
ofVec2f ofVec2f::getPerpendicular()
Return the normalized ofVec2f that is perpendicular to this vector (ie rotated 90 degrees and normalized).
Image courtesy of Wikipedia
ofVec2f v(2, 5);
ofVec2f u = v.getPerpendicular(); // u is (0.928, -0.371)
getRotated(...)
ofVec2f ofVec2f::getRotated(float angle)
Return a new ofVec2f that is the result of rotating this vector by angle degrees around the origin.
ofVec2f v1(1, 0);
ofVec2f v2 = v1.getRotated( 45 ); // v2 is (√2, √2)
ofVec3f v3 = v2.getRotated( 45 ); // v3 is (0, 1)
getRotated(...)
ofVec2f ofVec2f::getRotated(float angle, const ofVec2f &pivot)
Like getRotated but rotates around pivot rather than around the origin.
getRotatedRad(...)
ofVec2f ofVec2f::getRotatedRad(float angle)
Return a new ofVec2f that is the result of rotating this vector by angle radians around the origin.
ofVec2f v1(1, 0);
ofVec2f v2 = v1.getRotatedRad( PI/4 ); // v2 is (√2, √2)
ofVec3f v3 = v2.getRotated( PI/4 ); // v3 is (0, 1)
getRotatedRad(...)
ofVec2f ofVec2f::getRotatedRad(float angle, const ofVec2f &pivot)
Like getRotatedRad but rotates around pivot rather than around the origin.
getScaled(...)
ofVec2f ofVec2f::getScaled(const float length)
Return a new ofVec2f that is the result of scaling this vector up or down so that it has the requested length.
ofVec2f v1( 3, 4 ); // length is 5
ofVec2f v2 = v1.getScaled( 15 ); // ( 9, 12 ), length is now 15
interpolate(...)
ofVec2f ofVec2f::interpolate(const ofVec2f &pnt, float p)
Perform a linear interpolation of this vector's position towards pnt. p controls the amount to move towards pnt. p is normally between 0 and 1 and where 0 means stay the original position and 1 means move all the way to pnt, but you can also have p greater than 1 overshoot pnt, or less than 0 to move backwards away from pnt.
ofVec2f v1( 0, 5 );
ofVec2f v2( 10, 10 );
// go go gadget zeno
v1.interpolate( v2, 0.5 ); // v1 is now (5, 7.5)
v1.interpolate( v2, 0.5 ); // v1 is now (7.5, 8.75)
v1.interpolate( v2, 0.5 ); // v1 is now (8.75, 9.375)
v1.interpolate( v2, 0.5 ); // v1 is now (9.375, 9.6875)
length()
float ofVec2f::length()
Return the length (magnitude) of this vector.
ofVec2f v(3, 4);
float len = v.length(); // len is 5 (3,4,5 triangle)
length involves a square root calculation, which is one of the slowest things you can do in programming. If you don't need an exact number but rather just a rough idea of a length (for example when finding the shortest distance of a bunch of points to a reference point, where it doesn't matter exactly what the lengths are, you just want the shortest), you can use squareLength instead.
limit(...)
ofVec2f ofVec2f::limit(float max)
Restrict the length (magnitude) of this vector to a maximum of max units by scaling down if necessary.
ofVec2f v1(5, 1); // length is about 5.1
ofVec2f v2(2, 1); // length is about 2.2
v1.limit(3);
// v1 is now (2.9417, 0.58835) which has length of 3 in the same direction as at initialization
v2.limit(3);
// v2 is unchanged
map(...)
ofVec2f ofVec2f::map(const ofVec2f &origin, const ofVec2f &vx, const ofVec2f &vy)
Maps this vector from its default coordinate system -- origin (0,0), X direction (1,0), Y direction (0,1) -- to a new coordinate system defined with origin at origin, X direction vx, and Y direction vy.
In most case you want vx and vy to be perpendicular and of unit length; if they are not perpendicular you will have shearing as part of the mapping, and if they are not of unit length you will have scaling as part of the mapping.
match(...)
bool ofVec2f::match(const ofVec2f &vec, float tolerance=0.0001)
Returns true if each component is close enough to its corresponding component in vec, where what is close enough is determined by the value of tolerance:
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(40.01, 19.999);
// v1.match(v2, 0.1) returns true
// v1.match(v2, 0.001) returns false
This is handy if, for example, you want to find out when a point becomes close enough to another point to trigger an event.
middle(...)
ofVec2f ofVec2f::middle(const ofVec2f &pnt)
Set this vector to the midpoint between itself and pnt.
ofVec2f v1( 0, 5 );
ofVec2f v2( 10, 10 );
// go go gadget zeno
v1.middle( v2 ); // v1 is now (5, 7.5)
v1.middle( v2 ); // v1 is now (7.5, 8.75)
v1.middle( v2 ); // v1 is now (8.75, 9.375)
v1.middle( v2 ); // v1 is now (9.375, 9.6875)
normalize()
ofVec2f ofVec2f::normalize()
Normalize the vector.
Normalizing means to scale the vector so that its length (magnitude) is exactly 1, at which stage all that is left is the direction. A normalized vector is usually called a unit vector, and can be used to represent a pure direction (heading).
ofVec2f v1(5, 0);
v1.normalize(); // v2 is now (1, 0)
ofVec2f v2(5, 5);
v2.normalize(); // v2 is now (√2, √2)
operator!=(...)
bool ofVec2f::operator!=(const ofVec2f &vec)
Returns true if any component is different to its corresponding component in vec, ie if x != vec.x or y != vec.y; otherwise returns false.
ofVec2f v1(40, 20);
ofVec2f v2(50, 30);
ofVec2f v3(40, 20);
// ( v1 != v2 ) is true
// ( v1 != v3 ) is false
operator*(...)
ofVec2f ofVec2f::operator*(const float f)
Return a new ofVec2f that is this vector scaled by multiplying both x and y members by f.
ofVec2f v1(2, 5);
ofVec2f v2 = v1 * 4; // (8, 20)
operator*=(...)
ofVec2f ofVec2f::operator*=(const float f)
Scale this vector by multiplying both x and y members by f.
ofVec2f v1(2, 5);
v1 *= 4; // (8, 20)
operator+(...)
ofVec2f ofVec2f::operator+(const ofVec2f &vec)
Super easy vector addition. Returns a new vector (x+vec.x,y+vec.y).
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(25, 50);
ofVec3f v3 = v1 + v2; // v3 is (65, 70)
operator+(...)
ofVec2f ofVec2f::operator+(const float f)
Returns a new vector with a float value f added to both x and y members.
ofVec2f v1(2, 5);
ofVec2f v2 = v1 + 10; // (12, 15)
operator+=(...)
ofVec2f ofVec2f::operator+=(const ofVec2f &vec)
Super easy addition assignment. Adds vec.x to x, and adds vec.y to y.
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(25, 50);
v1 += v2; // v1 is (65, 70)
operator+=(...)
ofVec2f ofVec2f::operator+=(const float f)
Adds a float value f to both x and y members.
ofVec2f v1(2, 5);
v1 += 10; // (12, 15)
operator-(...)
ofVec2f ofVec2f::operator-(const ofVec2f &vec)
Super easy vector subtraction. Returns a new vector (x-vec.x,y-vec.y).
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(25, 50);
ofVec3f v3 = v1 - v2; // v3 is (15, -30)
operator-(...)
ofVec2f ofVec2f::operator-(const float f)
Returns a new vector with a float value f subtracted from both x and y members.
ofVec2f v1(2, 5);
ofVec2f v2 = v1 - 10; // (-8, -5)
operator-()
ofVec2f ofVec2f::operator-()
Returns a new ofVec2f that is the inverted version (mirrored in X and Y) of this vector.
ofVec2f v1(2, 5);
ofVec2f v2 = -v1; // (-2, -5)
operator-=(...)
ofVec2f ofVec2f::operator-=(const ofVec2f &vec)
Super easy subtraction assignment. Subtracts vec.x from x, and subtracts vec.y from y.
ofVec2f v1 = ofVec2f(40, 20);
ofVec2f v2 = ofVec2f(25, 50);
v1 -= v2; // v1 is (15, -30)
operator-=(...)
ofVec2f ofVec2f::operator-=(const float f)
Subtract a float value f from both x and y members.
ofVec2f v1(2, 5);
v1 -= 10; // (-8, -5)
operator/(...)
ofVec2f ofVec2f::operator/(const float f)
Return a new ofVec2f that is this vector scaled by dividing both x and y members by f.
ofVec2f v1(2, 5);
ofVec2f v2 = v1 / 4; // (0.5, 1.25)
operator/=(...)
ofVec2f ofVec2f::operator/=(const float f)
Scale this vector by dividing both x and y members by f.
ofVec2f v1(2, 5);
v1 /= 4; // (0.5, 1.25)
operator==(...)
bool ofVec2f::operator==(const ofVec2f &vec)
Returns true if each component is the same as the corresponding component in vec, ie if x == vec.x and y == vec.y; otherwise returns false.
ofVec2f v1(40, 20);
ofVec2f v2(50, 30);
ofVec2f v3(40, 20);
// ( v1 == v2 ) is false
// ( v1 == v3 ) is true
perpendicular()
ofVec2f ofVec2f::perpendicular()
Set this vector to its own normalized perpendicular (by rotating 90 degrees and normalizing).
Image courtesy of Wikipedia
ofVec2f v(2, 5);
v.perpendicular(); // v is (0.928, -0.371)
rotate(...)
ofVec2f ofVec2f::rotate(float angle)
Rotate this vector by angle degrees around the origin.
ofVec2f v1(1, 0);
v1.rotate( 45 ); // (√2, √2)
v1.rotate( 45 ); // (0, 1)
rotate(...)
ofVec2f ofVec2f::rotate(float angle, const ofVec2f &pivot)
Like rotate but rotates around pivot rather than around the origin.
rotateRad(...)
ofVec2f ofVec2f::rotateRad(float angle)
Rotate this vector by angle radians around the origin.
ofVec2f v1(1, 0);
v1.rotate( PI/4 ); // (√2, √2)
v1.rotate( PI/4 ); // (0, 1)
rotateRad(...)
ofVec2f ofVec2f::rotateRad(float angle, const ofVec2f &pivot)
Like rotateRad but rotates around pivot rather than around the origin.
scale(...)
ofVec2f ofVec2f::scale(const float length)
Scales this vector up or down so that it has the requested length.
ofVec2f v1( 3, 4 ); // length is 5
v1.scale( 15 ); // v1 is now (9, 12), with length 15
set(...)
void ofVec2f::set(float _x, float _y)
Set x and y components of this vector with just one function call.
ofVec2f v1;
v1.set(40, 20);
set(...)
void ofVec2f::set(const ofVec2f &vec)
Set the x and y components of this vector by copying the corresponding values from vec.
ofVec2f v1(40, 20);
ofVec2f v2;
v2.set(v1); // v2.x is 40, v2.y is 20
squareDistance(...)
float ofVec2f::squareDistance(const ofVec2f &pnt)
Treats both this vector and pnt as points in 2D space, and calculates and returns the squared distance between them.
ofVec2f p1( 3, 4 );
ofVec2f p2( 6, 8 );
float distance = p1.distance( p2 ); // distance is 5
Use as a much faster alternative to distance if you don't need to know an exact number but rather just a rough idea of distance (for example when finding the shortest distance of a bunch of points to a reference point, where it doesn't matter exactly what the distances are, you just want the shortest). It avoids the square root calculation that is ordinarily required to calculate a length.
squareLength()
float ofVec2f::squareLength()
Return the squared length (squared magnitude) of this vector.
ofVec2f v(3, 4);
float len = v.length(); // len is 5 (3,4,5 triangle)
Use as a much faster alternative to length if you don't need to know an accurate length but rather just a rough idea of a length (for example when finding the shortest distance of a bunch of points to a reference point, where it doesn't matter exactly what the lengths are, you just want the shortest). It avoids the square root calculation that is ordinarily required to calculate a length.