vec Plane::ClosestPoint(const LineSegment &lineSegment) const
{
/*
///@todo Output parametric d as well.
float d;
if (lineSegment.Intersects(*this, &d))
return lineSegment.GetPoint(d);
else
if (Distance(lineSegment.a) < Distance(lineSegment.b))
return Project(lineSegment.a);
else
return Project(lineSegment.b);
*/
assume(lineSegment.IsFinite());
assume(!IsDegenerate());
float aDist = Dot(normal, lineSegment.a);
float bDist = Dot(normal, lineSegment.b);
float denom = bDist - aDist;
if (EqualAbs(denom, 0.f))
return Project(Abs(aDist) < Abs(bDist) ? lineSegment.a : lineSegment.b); // Project()ing the result here is not strictly necessary,
// but done for numerical stability, so that Plane::Contains()
// will return true for the returned point.
else
{
///@todo Output parametric t along the ray as well.
float t = (d - Dot(normal, lineSegment.a)) / (bDist - aDist);
t = Clamp01(t);
// Project()ing the result here is necessary only if we clamped, but done for numerical stability, so that Plane::Contains() will
// return true for the returned point.
return Project(lineSegment.GetPoint(t));
}
}
static Float _ModifyHairShadowTransparencyFn(HairVideoPost* vp, Int32 oindex, HairMaterialData* mat, RayObject* ro, HairObject* op, HairGuides* guides, BaseList2D* bl, Float32* thk, VolumeData* vd, Int32 cpu, Int32 lid, Int32 seg, Int32 p, Float lined, const Vector& linep, const Vector& n, const Vector& lp, const Vector& huv, const RayHitID& ply_id, RayLight* light, Float trans)
{
HairRenderingTag* hrt = (HairRenderingTag*)bl->GetNodeData();
if (light) // shadow call
trans = (Float) 1.0 - Clamp01(((Float) 1.0 - Clamp01(trans)) * hrt->m_Shadow);
else
trans = (Float) 1.0 - Clamp01(((Float) 1.0 - Clamp01(trans)) * hrt->m_Trans);
if (hrt->m_Depth > 1)
{
Float depth = Float(1 + (seg % hrt->m_Depth)) / Float(hrt->m_Depth);
trans = 1.0 - ((1.0 - trans) * depth);
}
return trans;
}
void SaveSummary(const std::string &fname, Result &result, Config &config)
{
const float fnorm = 2.f / sqrtf(result.npoints);
const float rnorm = 1.f / sqrtf(2.f / (SQRT3 * result.npoints));
const int csize = 512; // Composition cell size
const double dashes[] = { 6.0, 3.0 };
cairo_surface_t *surface =
cairo_pdf_surface_create(fname.c_str(), 2*csize, 1.5*csize);
cairo_pdf_surface_restrict_to_version(surface, CAIRO_PDF_VERSION_1_4);
cairo_t *cr = cairo_create(surface);
unsigned char *imgdata = NULL;
cairo_surface_t *image = NULL;
// Draw points
const float radius = 2.0;
cairo_identity_matrix(cr);
cairo_set_source_rgba(cr, 0, 0, 0, 1);
for (int i = 0; i < result.points.size(); ++i) {
float x = result.points[i].x * csize;
float y = (1.f - result.points[i].y) * csize;
cairo_arc(cr, x, y, radius, 0, TWOPI);
cairo_fill(cr);
}
// Draw radial power reference level
cairo_identity_matrix(cr);
cairo_set_source_rgba(cr, 0.6, 0.6, 0.6, 1);
cairo_set_line_width(cr, 1.0);
cairo_set_dash(cr, dashes, 2, 0);
const float rpref = 1.f - (1.f - config.fymin) / (config.fymax - config.fymin);
cairo_move_to(cr, csize, csize + rpref*csize/2);
cairo_line_to(cr, 2*csize, csize + rpref*csize/2);
cairo_stroke(cr);
// Draw radial power
cairo_identity_matrix(cr);
cairo_set_source_rgba(cr, 0, 0, 0, 1);
cairo_set_line_width(cr, 1.0);
cairo_set_dash(cr, NULL, 0, 0);
for (int i = 0; i < result.rp.size(); ++i) {
float x = i / (float) result.rp.size();
float y = 1.f - (result.rp[i] - config.fymin) / (config.fymax - config.fymin);
Clamp01(y);
if (i == 0)
cairo_move_to(cr, csize + x*csize, csize + y*csize/2);
else
cairo_line_to(cr, csize + x*csize, csize + y*csize/2);
}
cairo_stroke(cr);
// Draw spectrum
int stride = cairo_format_stride_for_width(CAIRO_FORMAT_RGB24,
result.spectrum.width);
result.spectrum.GetRGBA(imgdata);
image = cairo_image_surface_create_for_data(imgdata, CAIRO_FORMAT_RGB24,
result.spectrum.width,
result.spectrum.height,
stride);
cairo_identity_matrix(cr);
cairo_translate(cr, csize, 0);
cairo_scale(cr, csize / (float) result.spectrum.width,
csize / (float) result.spectrum.height);
cairo_set_source_surface(cr, image, 0, 0);
cairo_paint(cr);
// Draw RDF reference level
cairo_identity_matrix(cr);
cairo_set_source_rgba(cr, 0.6, 0.6, 0.6, 1);
cairo_set_line_width(cr, 1.0);
cairo_set_dash(cr, dashes, 2, 0);
const float rdfref = 1.f - (1.f - config.rymin) / (config.rymax - config.rymin);
cairo_move_to(cr, 0, csize + rdfref*csize/2);
cairo_line_to(cr, csize, csize + rdfref*csize/2);
cairo_stroke(cr);
// Draw RDF
cairo_identity_matrix(cr);
cairo_set_source_rgba(cr, 0, 0, 0, 1);
cairo_set_line_width(cr, 1.0);
cairo_set_dash(cr, NULL, 0, 0);
for (int i = 0; i < result.rdf.size(); ++i) {
float x = i / (float) result.rdf.size();
float y = 1.f - (result.rdf[i] - config.rymin) / (config.rymax - config.rymin);
Clamp01(y);
if (i == 0)
cairo_move_to(cr, x*csize, csize + y*csize/2);
else
cairo_line_to(cr, x*csize, csize + y*csize/2);
}
cairo_stroke(cr);
// Draw separators
cairo_identity_matrix(cr);
cairo_set_line_width(cr, 1.0);
cairo_set_source_rgba(cr, 0, 0, 0, 1);
cairo_move_to(cr, 0, csize);
cairo_line_to(cr, 2*csize, csize);
cairo_stroke(cr);
cairo_move_to(cr, csize, 0);
cairo_line_to(cr, csize, 1.5*csize);
cairo_stroke(cr);
// Draw labels
cairo_identity_matrix(cr);
cairo_set_font_size(cr, 12.0);
cairo_select_font_face(cr, "Sans", CAIRO_FONT_SLANT_NORMAL,
CAIRO_FONT_WEIGHT_NORMAL);
cairo_set_source_rgba(cr, 0, 0, 0, 1);
cairo_move_to(cr, 0.0125 * csize, 1.025 * csize);
cairo_show_text(cr, "RDF");
cairo_stroke(cr);
cairo_move_to(cr, 1.0125 * csize, 1.025 * csize);
cairo_show_text(cr, "Power Spectrum");
cairo_stroke(cr);
// Draw stats box
#ifdef PSA_HAS_CGAL
int nlines = 5;
#else
int nlines = 4;
#endif
nlines += (result.nsets > 1);
double offset = 0.03;
double bsize[] = { 0.33 * csize, (nlines * offset + 0.01) * csize };
double banchor = 0.0125 * csize;
cairo_set_source_rgba(cr, 0.0, 0.0, 0.0, 0.7);
cairo_rectangle(cr, banchor, banchor, bsize[0], bsize[1]);
cairo_fill(cr);
// Draw stats and corresponding labels
cairo_set_source_rgba(cr, 1.0, 1.0, 1.0, 1.0);
cairo_set_font_size(cr, 12.0);
cairo_select_font_face(cr, "monospace", CAIRO_FONT_SLANT_NORMAL,
CAIRO_FONT_WEIGHT_NORMAL);
const int len = 128;
char label[len];
double tanchor[2] = { 1.75 * banchor, 0.9 * banchor };
int i = 1;
if (result.nsets > 1) {
snprintf(label, len, "Averaged over %d sets", result.nsets);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize);
cairo_show_text(cr, label);
++i;
}
snprintf(label, len, "Gbl. Mindist %.5f", result.stats.mindist * rnorm);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize); ++i;
cairo_show_text(cr, label);
snprintf(label, len, "Avg. Mindist %.5f", result.stats.avgmindist * rnorm);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize); ++i;
cairo_show_text(cr, label);
#ifdef PSA_HAS_CGAL
snprintf(label, len, "Orient. order %.5f", result.stats.orientorder);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize); ++i;
cairo_show_text(cr, label);
#endif
snprintf(label, len, "Eff. Nyquist %.5f", result.stats.effnyquist * fnorm);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize); ++i;
cairo_show_text(cr, label);
snprintf(label, len, "Oscillations %.5f", result.stats.oscillations);
cairo_move_to(cr, tanchor[0], tanchor[1] + i * offset * csize); ++i;
cairo_show_text(cr, label);
cairo_stroke(cr);
// Save and clean up
cairo_show_page(cr);
cairo_surface_destroy(image);
if (imgdata) delete[] imgdata;
cairo_destroy(cr);
cairo_surface_destroy(surface);
}
///\todo Enable this codepath. This if rom Geometric Tools for Computer Graphics,
/// but the algorithm in the book is broken and does not take into account the
/// direction of the gradient to determine the proper region of intersection.
/// Instead using a slower code path above.
/// [groupSyntax]
float3 Triangle::ClosestPoint(const LineSegment &lineSegment, float3 *otherPt) const
{
float3 e0 = b - a;
float3 e1 = c - a;
float3 v_p = a - lineSegment.a;
float3 d = lineSegment.b - lineSegment.a;
// Q(u,v) = a + u*e0 + v*e1
// L(t) = ls.a + t*d
// Minimize the distance |Q(u,v) - L(t)|^2 under u >= 0, v >= 0, u+v <= 1, t >= 0, t <= 1.
float v_p_dot_e0 = Dot(v_p, e0);
float v_p_dot_e1 = Dot(v_p, e1);
float v_p_dot_d = Dot(v_p, d);
float3x3 m;
m[0][0] = Dot(e0, e0); m[0][1] = Dot(e0, e1); m[0][2] = -Dot(e0, d);
m[1][0] = m[0][1]; m[1][1] = Dot(e1, e1); m[1][2] = -Dot(e1, d);
m[2][0] = m[0][2]; m[2][1] = m[1][2]; m[2][2] = Dot(d, d);
float3 B(-v_p_dot_e0, -v_p_dot_e1, v_p_dot_d);
float3 uvt;
bool success = m.SolveAxb(B, uvt);
if (!success)
{
float t1, t2, t3;
float s1, s2, s3;
LineSegment e1 = Edge(0);
LineSegment e2 = Edge(1);
LineSegment e3 = Edge(2);
float d1 = e1.Distance(lineSegment, &t1, &s1);
float d2 = e2.Distance(lineSegment, &t2, &s2);
float d3 = e3.Distance(lineSegment, &t3, &s3);
if (d1 < d2 && d1 < d3)
{
if (otherPt)
*otherPt = lineSegment.GetPoint(s1);
return e1.GetPoint(t1);
}
else if (d2 < d3)
{
if (otherPt)
*otherPt = lineSegment.GetPoint(s2);
return e2.GetPoint(t2);
}
else
{
if (otherPt)
*otherPt = lineSegment.GetPoint(s3);
return e3.GetPoint(t3);
}
}
if (uvt.x < 0.f)
{
// Clamp to u == 0 and solve again.
float m_00 = m[2][2];
float m_01 = -m[1][2];
float m_10 = -m[2][1];
float m_11 = m[1][1];
float det = m_00 * m_11 - m_01 * m_10;
float v = m_00 * B[1] + m_01 * B[2];
float t = m_10 * B[1] + m_11 * B[2];
v /= det;
t /= det;
if (v < 0.f)
{
// Clamp to v == 0 and solve for t.
t = B[2] / m[2][2];
t = Clamp01(t); // The solution for t must also be in the range [0,1].
// The solution is (u,v,t)=(0,0,t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return a;
}
else if (v > 1.f)
{
// Clamp to v == 1 and solve for t.
t = (B[2] - m[2][1]) / m[2][2];
t = Clamp01(t);
// The solution is (u,v,t)=(0,1,t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return c; // == a + v*e1
}
else if (t < 0.f)
{
// Clamp to t == 0 and solve for v.
v = B[1] / m[1][1];
// mathassert(EqualAbs(v, Clamp01(v)));
v = Clamp01(v); // The solution for v must also be in the range [0,1]. TODO: Is this guaranteed by the above?
// The solution is (u,v,t)=(0,v,0).
if (otherPt)
*otherPt = lineSegment.a;
return a + v * e1;
}
else if (t > 1.f)
{
// Clamp to t == 1 and solve for v.
v = (B[1] - m[1][2]) / m[1][1];
// mathassert(EqualAbs(v, Clamp01(v)));
v = Clamp01(v); // The solution for v must also be in the range [0,1]. TODO: Is this guaranteed by the above?
// The solution is (u,v,t)=(0,v,1).
if (otherPt)
*otherPt = lineSegment.b;
return a + v * e1;
}
else
{
// The solution is (u,v,t)=(0,v,t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return a + v * e1;
}
}
else if (uvt.y < 0.f)
{
// Clamp to v == 0 and solve again.
float m_00 = m[2][2];
float m_01 = -m[0][2];
float m_10 = -m[2][0];
float m_11 = m[0][0];
float det = m_00 * m_11 - m_01 * m_10;
float u = m_00 * B[0] + m_01 * B[2];
float t = m_10 * B[0] + m_11 * B[2];
u /= det;
t /= det;
if (u < 0.f)
{
// Clamp to u == 0 and solve for t.
t = B[2] / m[2][2];
t = Clamp01(t); // The solution for t must also be in the range [0,1].
// The solution is (u,v,t)=(0,0,t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return a;
}
else if (u > 1.f)
{
// Clamp to u == 1 and solve for t.
t = (B[2] - m[2][0]) / m[2][2];
t = Clamp01(t); // The solution for t must also be in the range [0,1].
// The solution is (u,v,t)=(1,0,t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return b;
}
else if (t < 0.f)
{
// Clamp to t == 0 and solve for u.
u = B[0] / m[0][0];
// mathassert(EqualAbs(u, Clamp01(u)));
u = Clamp01(u); // The solution for u must also be in the range [0,1].
if (otherPt)
*otherPt = lineSegment.a;
return a + u * e0;
}
else if (t > 1.f)
{
// Clamp to t == 1 and solve for u.
u = (B[0] - m[0][2]) / m[0][0];
// mathassert(EqualAbs(u, Clamp01(u)));
u = Clamp01(u); // The solution for u must also be in the range [0,1].
if (otherPt)
*otherPt = lineSegment.b;
return a + u * e0;
}
else
{
// The solution is (u, 0, t).
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return a + u * e0;
}
}
else if (uvt.z < 0.f)
{
if (otherPt)
*otherPt = lineSegment.a;
// Clamp to t == 0 and solve again.
float m_00 = m[1][1];
float m_01 = -m[0][1];
float m_10 = -m[1][0];
float m_11 = m[0][0];
float det = m_00 * m_11 - m_01 * m_10;
float u = m_00 * B[0] + m_01 * B[1];
float v = m_10 * B[0] + m_11 * B[1];
u /= det;
v /= det;
if (u < 0.f)
{
// Clamp to u == 0 and solve for v.
v = B[1] / m[1][1];
v = Clamp01(v);
return a + v*e1;
}
else if (v < 0.f)
{
// Clamp to v == 0 and solve for u.
u = B[0] / m[0][0];
u = Clamp01(u);
return a + u*e0;
}
else if (u+v > 1.f)
{
// Set v = 1-u and solve again.
// u = (B[0] - m[0][0]) / (m[0][0] - m[0][1]);
// mathassert(EqualAbs(u, Clamp01(u)));
// u = Clamp01(u); // The solution for u must also be in the range [0,1].
// return a + u*e0;
// Clamp to v = 1-u and solve again.
float m_00 = m[2][2];
float m_01 = m[1][2] - m[0][2];
float m_10 = m_01;
float m_11 = m[0][0] + m[1][1] - 2.f * m[0][1];
float det = m_00 * m_11 - m_01 * m_10;
float b0 = m[1][1] - m[0][1] + v_p_dot_e1 - v_p_dot_e0;
float b1 = -m[1][2] + v_p_dot_d;
float u = m_00 * b0 + m_01 * b1;
u /= det;
u = Clamp01(u);
float t = m_10 * b0 + m_11 * b1;
t /= det;
t = Clamp01(t);
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
return a + u*e0 + (1.f-u)*e1;
}
else
{
// The solution is (u, v, 0)
return a + u * e0 + v * e1;
}
}
else if (uvt.z > 1.f)
{
if (otherPt)
*otherPt = lineSegment.b;
// Clamp to t == 1 and solve again.
float m_00 = m[1][1];
float m_01 = -m[0][1];
float m_10 = -m[1][0];
float m_11 = m[0][0];
float det = m_00 * m_11 - m_01 * m_10;
float u = m_00 * (B[0]-m[0][2]) + m_01 * (B[1]-m[1][2]);
float v = m_10 * (B[0]-m[0][2]) + m_11 * (B[1]-m[1][2]);
u /= det;
v /= det;
if (u < 0.f)
{
// Clamp to u == 0 and solve again.
v = (B[1] - m[1][2]) / m[1][1];
v = Clamp01(v);
return a + v*e1;
}
else if (u > 1.f)
{
// Clamp to u == 1 and solve again.
v = (B[1] - m[1][0] - m[1][2]) / m[1][1];
v = Clamp01(v); // The solution for v must also be in the range [0,1]. TODO: Is this guaranteed by the above?
// The solution is (u,v,t)=(1,v,1).
return a + e0 + v*e1;
}
else if (u+v > 1.f)
{
// Set v = 1-u and solve again.
// Q(u,1-u) = a + u*e0 + e1 - u*e1 = a+e1 + u*(e0-e1)
// L(1) = ls.a + t*d = ls.b
// Minimize the distance |Q(u,1-u) - L(1)| = |a+e1+ls.b + u*(e0-e1)|
// |K + u*(e0-e1)|^2 = (K,K) + 2*u(K,e0-e1) + u^2 * (e0-e1,e0-e1)
// grad = 2*(K,e0-e1) + 2*u*(e0-e1,e0-e1) == 0
// u == (K,e1-e0) / (e0-e1,e0-e1)
u = (B[0] - m[0][1] - m[0][2]) / (m[0][0] - m[0][1]);
// u = Dot(a + e1 + lineSegment.b, e1 - e0) / Dot(e0-e1, e0-e1);
// mathassert(EqualAbs(u, Clamp01(u)));
u = Clamp01(u);
return a + u*e0 + (1-u)*e1;
}
else
{
// The solution is (u, v, 1)
return a + u*e0 + v*e1;
}
}
else if (uvt.x + uvt.y > 1.f)
{
// Clamp to v = 1-u and solve again.
float m_00 = m[2][2];
float m_01 = m[1][2] - m[0][2];
float m_10 = m_01;
float m_11 = m[0][0] + m[1][1] - 2.f * m[0][1];
float det = m_00 * m_11 - m_01 * m_10;
float b0 = m[1][1] - m[0][1] + v_p_dot_e1 - v_p_dot_e0;
float b1 = -m[1][2] + v_p_dot_d;
float u = m_00 * b0 + m_01 * b1;
float t = m_10 * b0 + m_11 * b1;
u /= det;
t /= det;
t = Clamp01(t);
if (otherPt)
*otherPt = lineSegment.GetPoint(t);
if (u < 0.f)
{
// The solution is (u,v,t)=(0,1,t)
return c;
}
if (u > 1.f)
{
// The solution is (u,v,t)=(1,0,t)
return b;
}
mathassert(t >= 0.f);
mathassert(t <= 1.f);
return a + u*e0 + (1.f-u)*e1;
}
else // All parameters are within range, so the triangle and the line segment intersect, and the intersection point is the closest point.
{
if (otherPt)
*otherPt = lineSegment.GetPoint(uvt.z);
return a + uvt.x * e0 + uvt.y * e1;
}
}
