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/**
* N-dimensional half-open interval [a, b[.
*
* Copyright: Copyright Guillaume Piolat 2015-2021.
* Copyright Ahmet Sait 2021.
* Copyright Ryan Roden-Corrent 2016.
* Copyright Nathan Sashihara 2018.
* Copyright Colden Cullen 2014.
*
* License: $(LINK2 http://www.boost.org/LICENSE_1_0.txt, Boost License 1.0)
*/
module dplug.math.box;
import std.math,
std.traits;
import dplug.math.vector;
/// N-dimensional half-open interval [a, b[.
struct Box(T, int N)
{
static assert(N > 0);
public
{
alias bound_t = Vector!(T, N);
bound_t min; // not enforced, the box can have negative volume
bound_t max;
/// Construct a box which extends between 2 points.
/// Boundaries: min is inside the box, max is just outside.
@nogc this(bound_t min_, bound_t max_) pure nothrow
{
min = min_;
max = max_;
}
static if (N == 1)
{
@nogc this(T min_, T max_) pure nothrow
{
min.x = min_;
max.x = max_;
}
}
static if (N == 2)
{
@nogc this(T min_x, T min_y, T max_x, T max_y) pure nothrow
{
min = bound_t(min_x, min_y);
max = bound_t(max_x, max_y);
}
}
static if (N == 3)
{
@nogc this(T min_x, T min_y, T min_z, T max_x, T max_y, T max_z) pure nothrow
{
min = bound_t(min_x, min_y, min_z);
max = bound_t(max_x, max_y, max_z);
}
}
@property
{
/// Returns: Dimensions of the box.
@nogc bound_t size() pure const nothrow
{
return max - min;
}
/// Sets size of the box assuming min point is the pivot.
/// Returns: Dimensions of the box.
@nogc bound_t size(bound_t value) pure nothrow
{
max = min + value;
return value;
}
/// Returns: Center of the box.
@nogc bound_t center() pure const nothrow
{
return (min + max) / 2;
}
static if (N >= 1)
{
/// Returns: Width of the box, always applicable.
@nogc T width() pure const nothrow @property
{
return max.x - min.x;
}
/// Sets width of the box assuming min point is the pivot.
/// Returns: Width of the box, always applicable.
@nogc T width(T value) pure nothrow @property
{
max.x = min.x + value;
return value;
}
}
static if (N >= 2)
{
/// Returns: Height of the box, if applicable.
@nogc T height() pure const nothrow @property
{
return max.y - min.y;
}
/// Sets height of the box assuming min point is the pivot.
/// Returns: Height of the box, if applicable.
@nogc T height(T value) pure nothrow @property
{
max.y = min.y + value;
return value;
}
}
static if (N >= 3)
{
/// Returns: Depth of the box, if applicable.
@nogc T depth() pure const nothrow @property
{
return max.z - min.z;
}
/// Sets depth of the box assuming min point is the pivot.
/// Returns: Depth of the box, if applicable.
@nogc T depth(T value) pure nothrow @property
{
max.z = min.z + value;
return value;
}
}
/// Returns: Signed volume of the box.
@nogc T volume() pure const nothrow
{
T res = 1;
bound_t size = size();
for(int i = 0; i < N; ++i)
res *= size[i];
return res;
}
/// Returns: true if empty.
@nogc bool empty() pure const nothrow
{
bound_t size = size();
mixin(generateLoopCode!("if (min[@] == max[@]) return true;", N)());
return false;
}
}
/// Returns: true if it contains point.
@nogc bool contains(bound_t point) pure const nothrow
{
assert(isSorted());
for(int i = 0; i < N; ++i)
if ( !(point[i] >= min[i] && point[i] < max[i]) )
return false;
return true;
}
static if (N >= 2)
{
/// Returns: true if it contains point `x`, `y`.
@nogc bool contains(T x, T y) pure const nothrow
{
assert(isSorted());
if ( !(x >= min.x && x < max.x) )
return false;
if ( !(y >= min.y && y < max.y) )
return false;
return true;
}
}
static if (N >= 3)
{
/// Returns: true if it contains point `x`, `y`, `z`.
@nogc bool contains(T x, T y, T z) pure const nothrow
{
assert(isSorted());
if ( !(x >= min.x && x < max.x) )
return false;
if ( !(y >= min.y && y < max.y) )
return false;
if ( !(z >= min.z && z < max.z) )
return false;
return true;
}
}
/// Returns: true if it contains box other.
@nogc bool contains(Box other) pure const nothrow
{
assert(isSorted());
assert(other.isSorted());
mixin(generateLoopCode!("if ( (other.min[@] < min[@]) || (other.max[@] > max[@]) ) return false;", N)());
return true;
}
/// Euclidean squared distance from a point.
/// See_also: Numerical Recipes Third Edition (2007)
@nogc real squaredDistance(bound_t point) pure const nothrow
{
assert(isSorted());
real distanceSquared = 0;
for (int i = 0; i < N; ++i)
{
if (point[i] < min[i])
distanceSquared += (point[i] - min[i]) ^^ 2;
if (point[i] > max[i])
distanceSquared += (point[i] - max[i]) ^^ 2;
}
return distanceSquared;
}
/// Euclidean distance from a point.
/// See_also: squaredDistance.
@nogc real distance(bound_t point) pure const nothrow
{
return sqrt(squaredDistance(point));
}
/// Euclidean squared distance from another box.
/// See_also: Numerical Recipes Third Edition (2007)
@nogc real squaredDistance(Box o) pure const nothrow
{
assert(isSorted());
assert(o.isSorted());
real distanceSquared = 0;
for (int i = 0; i < N; ++i)
{
if (o.max[i] < min[i])
distanceSquared += (o.max[i] - min[i]) ^^ 2;
if (o.min[i] > max[i])
distanceSquared += (o.min[i] - max[i]) ^^ 2;
}
return distanceSquared;
}
/// Euclidean distance from another box.
/// See_also: squaredDistance.
@nogc real distance(Box o) pure const nothrow
{
return sqrt(squaredDistance(o));
}
/// Assumes sorted boxes.
/// This function deals with empty boxes correctly.
/// Returns: Intersection of two boxes.
@nogc Box intersection(Box o) pure const nothrow
{
assert(isSorted());
assert(o.isSorted());
// Return an empty box if one of the boxes is empty
if (empty())
return this;
if (o.empty())
return o;
Box result = void;
for (int i = 0; i < N; ++i)
{
T maxOfMins = (min.v[i] > o.min.v[i]) ? min.v[i] : o.min.v[i];
T minOfMaxs = (max.v[i] < o.max.v[i]) ? max.v[i] : o.max.v[i];
result.min.v[i] = maxOfMins;
result.max.v[i] = minOfMaxs >= maxOfMins ? minOfMaxs : maxOfMins;
}
return result;
}
/// Assumes sorted boxes.
/// This function deals with empty boxes correctly.
/// Returns: Intersection of two boxes.
@nogc bool intersects(Box other) pure const nothrow
{
Box inter = this.intersection(other);
return inter.isSorted() && !inter.empty();
}
/// Extends the area of this Box.
@nogc Box grow(bound_t space) pure const nothrow
{
Box res = this;
res.min -= space;
res.max += space;
return res;
}
/// Shrink the area of this Box. The box might became unsorted.
@nogc Box shrink(bound_t space) pure const nothrow
{
return grow(-space);
}
/// Extends the area of this Box.
@nogc Box grow(T space) pure const nothrow
{
return grow(bound_t(space));
}
/// Translate this Box.
@nogc Box translate(bound_t offset) pure const nothrow
{
return Box(min + offset, max + offset);
}
/// Scale the box by factor `scale`, and round the result to integer if needed.
@nogc Box scaleByFactor(float scale) const nothrow
{
Box res;
static if (isFloatingPoint!T)
{
res.min.x = min.x * scale;
res.min.y = min.y * scale;
res.max.x = max.x * scale;
res.max.y = max.y * scale;
}
else
{
res.min.x = cast(T)( round(min.x * scale) );
res.min.y = cast(T)( round(min.y * scale) );
res.max.x = cast(T)( round(max.x * scale) );
res.max.y = cast(T)( round(max.y * scale) );
}
return res;
}
static if (N == 2) // useful for UI that have horizontal and vertical scale
{
/// Scale the box by factor `scaleX` horizontally and `scaleY` vetically.
/// Round the result to integer if needed.
@nogc Box scaleByFactor(float scaleX, float scaleY) const nothrow
{
Box res;
static if (isFloatingPoint!T)
{
res.min.x = min.x * scaleX;
res.min.y = min.y * scaleY;
res.max.x = max.x * scaleX;
res.max.y = max.y * scaleY;
}
else
{
res.min.x = cast(T)( round(min.x * scaleX) );
res.min.y = cast(T)( round(min.y * scaleY) );
res.max.x = cast(T)( round(max.x * scaleX) );
res.max.y = cast(T)( round(max.y * scaleY) );
}
return res;
}
}
static if (N >= 2)
{
/// Translate this Box by `x`, `y`.
@nogc Box translate(T x, T y) pure const nothrow
{
Box res = this;
res.min.x += x;
res.min.y += y;
res.max.x += x;
res.max.y += y;
return res;
}
}
static if (N >= 3)
{
/// Translate this Box by `x`, `y`.
@nogc Box translate(T x, T y, T z) pure const nothrow
{
Box res = this;
res.min.x += x;
res.min.y += y;
res.min.z += z;
res.max.x += x;
res.max.y += y;
res.max.z += z;
return res;
}
}
/// Shrinks the area of this Box.
/// Returns: Shrinked box.
@nogc Box shrink(T space) pure const nothrow
{
return shrink(bound_t(space));
}
/// Expands the box to include point.
/// Returns: Expanded box.
@nogc Box expand(bound_t point) pure const nothrow
{
import vector = dplug.math.vector;
return Box(vector.minByElem(min, point), vector.maxByElem(max, point));
}
/// Expands the box to include another box.
/// This function deals with empty boxes correctly.
/// Returns: Expanded box.
@nogc Box expand(Box other) pure const nothrow
{
assert(isSorted());
assert(other.isSorted());
// handle empty boxes
if (empty())
return other;
if (other.empty())
return this;
Box result = void;
for (int i = 0; i < N; ++i)
{
T minOfMins = (min.v[i] < other.min.v[i]) ? min.v[i] : other.min.v[i];
T maxOfMaxs = (max.v[i] > other.max.v[i]) ? max.v[i] : other.max.v[i];
result.min.v[i] = minOfMins;
result.max.v[i] = maxOfMaxs;
}
return result;
}
/// Returns: true if each dimension of the box is >= 0.
@nogc bool isSorted() pure const nothrow
{
for(int i = 0; i < N; ++i)
{
if (min[i] > max[i])
return false;
}
return true;
}
/// Returns: Absolute value of the Box to ensure each dimension of the
/// box is >= 0.
@nogc Box abs() pure const nothrow
{
Box!(T, N) s = this;
for (int i = 0; i < N; ++i)
{
if (s.min.v[i] > s.max.v[i])
{
T tmp = s.min.v[i];
s.min.v[i] = s.max.v[i];
s.max.v[i] = tmp;
}
}
return s;
}
/// Assign with another box.
@nogc ref Box opAssign(U)(U x) nothrow if (isBox!U)
{
static if(is(U.element_t : T))
{
static if(U._size == _size)
{
min = x.min;
max = x.max;
}
else
{
static assert(false, "no conversion between boxes with different dimensions");
}
}
else
{
static assert(false, "no conversion from " ~ U.element_t.stringof ~ " to " ~ element_t.stringof);
}
return this;
}
/// Returns: true if comparing equal boxes.
@nogc bool opEquals(U)(U other) pure const nothrow if (is(U : Box))
{
return (min == other.min) && (max == other.max);
}
/// Cast to other box types.
@nogc U opCast(U)() pure const nothrow if (isBox!U)
{
U b = void;
for(int i = 0; i < N; ++i)
{
b.min[i] = cast(U.element_t)(min[i]);
b.max[i] = cast(U.element_t)(max[i]);
}
return b; // return a box where each element has been casted
}
static if (N == 2)
{
/// Helper function to create rectangle with a given point, width and height.
static @nogc Box rectangle(T x, T y, T width, T height) pure nothrow
{
return Box(x, y, x + width, y + height);
}
}
}
private
{
enum _size = N;
alias T element_t;
}
}
/// Instanciate to use a 2D box.
template box2(T)
{
alias Box!(T, 2) box2;
}
/// Instanciate to use a 3D box.
template box3(T)
{
alias Box!(T, 3) box3;
}
alias box2!int box2i; /// 2D box with integer coordinates.
alias box3!int box3i; /// 3D box with integer coordinates.
alias box2!float box2f; /// 2D box with float coordinates.
alias box3!float box3f; /// 3D box with float coordinates.
alias box2!double box2d; /// 2D box with double coordinates.
alias box3!double box3d; /// 3D box with double coordinates.
/// Returns: A 2D rectangle with point `x`,`y`, `width` and `height`.
box2i rectangle(int x, int y, int width, int height) pure nothrow @nogc
{
return box2i(x, y, x + width, y + height);
}
/// Returns: A 2D rectangle with point `x`,`y`, `width` and `height`.
box2f rectanglef(float x, float y, float width, float height) pure nothrow @nogc
{
return box2f(x, y, x + width, y + height);
}
/// Returns: A 2D rectangle with point `x`,`y`, `width` and `height`.
box2d rectangled(double x, double y, double width, double height) pure nothrow @nogc
{
return box2d(x, y, x + width, y + height);
}
unittest
{
box2i a = box2i(1, 2, 3, 4);
assert(a.width == 2);
assert(a.height == 2);
assert(a.volume == 4);
box2i b = box2i(vec2i(1, 2), vec2i(3, 4));
assert(a == b);
box3i q = box3i(-3, -2, -1, 0, 1, 2);
q.bound_t s = q.bound_t(11, 17, 19);
q.bound_t q_min = q.min;
assert((q.size = s) == s);
assert(q.size == s);
assert(q.min == q_min);
assert(q.max == q.min + s);
assert(q.max - q.min == s);
assert((q.width = s.z) == s.z);
assert(q.width == s.z);
assert(q.min.x == q_min.x);
assert(q.max.x == q.min.x + s.z);
assert(q.max.x - q.min.x == s.z);
assert((q.height = s.y) == s.y);
assert(q.height == s.y);
assert(q.min.y == q_min.y);
assert(q.max.y == q.min.y + s.y);
assert(q.max.y - q.min.y == s.y);
assert((q.depth = s.x) == s.x);
assert(q.depth == s.x);
assert(q.min.z == q_min.z);
assert(q.max.z == q.min.z + s.x);
assert(q.max.z - q.min.z == s.x);
assert(q.size == s.zyx);
box3i n = box3i(2, 1, 0, -1, -2, -3);
assert(n.abs == box3i(-1, -2, -3, 2, 1, 0));
box2f bf = cast(box2f)b;
assert(bf == box2f(1.0f, 2.0f, 3.0f, 4.0f));
box3f qf = box3f(-0, 1f, 2.5f, 3.25f, 5.125f, 7.0625f);
qf.bound_t sf = qf.bound_t(-11.5f, -17.25f, -19.125f);
qf.bound_t qf_min = qf.min;
assert((qf.size = sf) == sf);
assert(qf.size == sf);
assert(qf.min == qf_min);
assert(qf.max == qf.min + sf);
assert(qf.max - qf.min == sf);
assert((qf.width = sf.z) == sf.z);
assert(qf.width == sf.z);
assert(qf.min.x == qf_min.x);
assert(qf.max.x == qf.min.x + sf.z);
assert(qf.max.x - qf.min.x == sf.z);
assert((qf.height = sf.y) == sf.y);
assert(qf.height == sf.y);
assert(qf.min.y == qf_min.y);
assert(qf.max.y == qf.min.y + sf.y);
assert(qf.max.y - qf.min.y == sf.y);
assert((qf.depth = sf.x) == sf.x);
assert(qf.depth == sf.x);
assert(qf.min.z == qf_min.z);
assert(qf.max.z == qf.min.z + sf.x);
assert(qf.max.z - qf.min.z == sf.x);
assert(qf.size == sf.zyx);
box2i c = box2i(0, 0, 1,1);
assert(c.translate(vec2i(3, 3)) == box2i(3, 3, 4, 4));
assert(c.translate(3, 3) == box2i(3, 3, 4, 4));
assert(c.contains(vec2i(0, 0)));
assert(c.contains(0, 0));
assert(!c.contains(vec2i(1, 1)));
assert(!c.contains(1, 1));
assert(b.contains(b));
box2i d = c.expand(vec2i(3, 3));
assert(d.contains(vec2i(2, 2)));
assert(d == d.expand(d));
assert(!box2i(0, 0, 4, 4).contains(box2i(2, 2, 6, 6)));
assert(box2f(0, 0, 0, 0).empty());
assert(!box2f(0, 2, 1, 1).empty());
assert(!box2f(0, 0, 1, 1).empty());
assert(box2i(260, 100, 360, 200).intersection(box2i(100, 100, 200, 200)).empty());
// union with empty box is identity
assert(a.expand(box2i(10, 4, 10, 6)) == a);
// intersection with empty box is empty
assert(a.intersection(box2i(10, 4, 10, 6)).empty);
assert(box2i.rectangle(1, 2, 3, 4) == box2i(1, 2, 4, 6));
assert(rectangle(1, 2, 3, 4) == box2i(1, 2, 4, 6));
assert(rectanglef(1, 2, 3, 4) == box2f(1, 2, 4, 6));
assert(rectangled(1, 2, 3, 4) == box2d(1, 2, 4, 6));
assert(rectangle(10, 10, 20, 20).scaleByFactor(1.5f) == rectangle(15, 15, 30, 30));
assert(rectangle(10, 10, 20, 20).scaleByFactor(1.5f, 2.0f) == rectangle(15, 20, 30, 40));
}
/// True if `T` is a kind of Box
enum isBox(T) = is(T : Box!U, U...);
unittest
{
static assert( isBox!box2f);
static assert( isBox!box3d);
static assert( isBox!(Box!(real, 2)));
static assert(!isBox!vec2f);
}
/// Get the numeric type used to measure a box's dimensions.
alias DimensionType(T : Box!U, U...) = U[0];
///
unittest
{
static assert(is(DimensionType!box2f == float));
static assert(is(DimensionType!box3d == double));
}