From d3516b11559657935d70829c672f29393e857b8e Mon Sep 17 00:00:00 2001
From: rodri <rgl@antares-labs.eu>
Date: Mon, 20 May 2024 20:20:48 +0000
Subject: fix the perspective projection and add inverse xform functions.

---
 xform.c | 167 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 167 insertions(+)
 create mode 100644 xform.c

(limited to 'xform.c')

diff --git a/xform.c b/xform.c
new file mode 100644
index 0000000..aba2089
--- /dev/null
+++ b/xform.c
@@ -0,0 +1,167 @@
+#include <u.h>
+#include <libc.h>
+#include <thread.h>
+#include <draw.h>
+#include <memdraw.h>
+#include <geometry.h>
+#include "libobj/obj.h"
+#include "graphics.h"
+#include "internal.h"
+
+/*
+ * transforms p from e's reference frame into
+ * the world.
+ */
+Point3
+model2world(Entity *e, Point3 p)
+{
+	return invrframexform3(p, *e);
+}
+
+/*
+ * transforms p from the world reference frame
+ * to c's one (aka Viewing Coordinate System).
+ */
+Point3
+world2vcs(Camera *c, Point3 p)
+{
+	return rframexform3(p, *c);
+}
+
+/*
+ * projects p from the VCS to clip space, placing
+ * p.[xyz] ∈ (-∞,-w)∪[-w,w]∪(w,∞) where [-w,w]
+ * represents the visibility volume.
+ *
+ * the clipping planes are:
+ *
+ * 	|   -w   |   w   |
+ *	+----------------+
+ * 	| left   | right |
+ * 	| bottom | top   |
+ * 	| far    | near  |
+ */
+Point3
+vcs2clip(Camera *c, Point3 p)
+{
+	return xform3(p, c->proj);
+}
+
+Point3
+world2clip(Camera *c, Point3 p)
+{
+	return vcs2clip(c, world2vcs(c, p));
+}
+
+/*
+ * performs the perspective division, placing
+ * p.[xyz] ∈ [-1,1] and p.w = 1/z
+ * (aka Normalized Device Coordinates).
+ *
+ * p.w is kept as z⁻¹ so we can later do
+ * perspective-correct attribute interpolation.
+ */
+Point3
+clip2ndc(Point3 p)
+{
+	p.w = p.w == 0? 1: 1.0/p.w;
+	p.x *= p.w;
+	p.y *= p.w;
+	p.z *= p.w;
+	return p;
+}
+
+/*
+ * scales p to fit the destination viewport,
+ * placing p.x ∈ [0,width], p.y ∈ [0,height],
+ * p.z ∈ [0,1] and leaving p.w intact.
+ */
+Point3
+ndc2viewport(Framebuf *fb, Point3 p)
+{
+	Matrix3 view = {
+		Dx(fb->r)/2.0,             0,       0,       Dx(fb->r)/2.0,
+		0,            -Dy(fb->r)/2.0,       0,       Dy(fb->r)/2.0,
+		0,                         0, 1.0/2.0,             1.0/2.0,
+		0,                         0,       0,                   1,
+	};
+	double w;
+
+	w = p.w;
+	p.w = 1;
+	p = xform3(p, view);
+	p.w = w;
+	return p;
+}
+
+Point3
+viewport2ndc(Framebuf *fb, Point3 p)
+{
+	p.x = 2*p.x/Dx(fb->r) - 1;
+	p.y = 1 - 2*p.y/Dy(fb->r);
+	p.z = 2*p.z - 1;
+	p.w = 1;
+	return p;
+}
+
+Point3
+ndc2vcs(Camera *c, Point3 p)
+{
+	Matrix3 invproj;
+	Point3 np;
+
+	memmove(invproj, c->proj, 4*4*sizeof(double));
+	invm3(invproj);
+	np = xform3(p, invproj);
+	np.w = np.w == 0? 0: 1.0/np.w;
+	np.x *= np.w;
+	np.y *= np.w;
+	np.z *= np.w;
+	np.w = 1;
+	return np;
+}
+
+Point3
+viewport2vcs(Camera *c, Point3 p)
+{
+	return ndc2vcs(c, viewport2ndc(c->vp->getfb(c->vp), p));
+}
+
+Point3
+vcs2world(Camera *c, Point3 p)
+{
+	return invrframexform3(p, *c);
+}
+
+Point3
+viewport2world(Camera *c, Point3 p)
+{
+	return vcs2world(c, viewport2vcs(c, p));
+}
+
+void
+perspective(Matrix3 m, double fovy, double a, double n, double f)
+{
+	double cotan;
+
+	cotan = 1/tan(fovy/2);
+	identity3(m);
+	m[0][0] =  cotan/a;
+	m[1][1] =  cotan;
+	m[2][2] =  (f+n)/(f-n);
+	m[2][3] =  2*f*n/(f-n);
+	m[3][2] = -1;
+	m[3][3] = 0;
+}
+
+void
+orthographic(Matrix3 m, double l, double r, double b, double t, double n, double f)
+{
+	identity3(m);
+	m[0][0] =  2/(r-l);
+	m[1][1] =  2/(t-b);
+	m[2][2] =  2/(f-n);
+	m[0][3] = -(r+l)/(r-l);
+	m[1][3] = -(t+b)/(t-b);
+	m[2][3] = -(f+n)/(f-n);
+}
-- 
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